FDM-Net: A Multi-Level Feature Aggregation Network Based on Frequency-Decomposition for Hyperspectral Image Classification

Highlights

What are the main findings?

• Existing CNN–Mamba hybrid models for hyperspectral image classification usually feed the same mixed spectral–spatial features into both branches. This design may weaken the complementary roles of Mamba and convolution, because low-frequency contextual information and high-frequency structural details are not explicitly separated.
• FDM-Net addresses this issue by introducing a frequency-decomposition strategy before dual-branch feature modeling. Low-frequency features are processed by a Mamba-based branch to capture long-range dependencies, while high-frequency features are enhanced by the proposed Multi-level Feature Aggregation Module to preserve local spatial details.
• Experiments on five public hyperspectral datasets show that FDM-Net obtains competitive classification results in terms of OA, AA, and Kappa, indicating that separating and recombining frequency-specific features is useful for spectral–spatial representation learning.

What are the implications of the main findings?

• The results indicate that CNN and Mamba modules should not simply be combined in parallel with identical inputs. A more effective design is to assign different frequency components to the modeling branch that is better suited to them.
• Frequency Decomposition offers a simple but useful way to reduce feature interference in hybrid hyperspectral classifiers, especially when global context and fine spatial structures need to be preserved at the same time.
• This finding suggests that future hyperspectral image classification networks can benefit from considering the frequency characteristics of features, rather than only increasing network depth, attention modules, or branch complexity.

Abstract

Recently, integrating convolutional neural networks (CNNs) with Mamba has shown notable advantages in hyperspectral image classification. However, existing Mamba–CNN hybrid frameworks typically adopt a parallel-branch architecture where identical spectral–spatial information is fed into both branches, failing to rectify the inherent frequency-specific bias: Mamba tends to prioritize low-frequency information, while CNNs excel at capturing high-frequency details. Existing convolutional architectures often fail to effectively exploit the multi-level interactions among spectral–spatial features. To handle these limitations, a novel multi-level Aggregation Network based on Frequency Decomposition (FDM-Net) is proposed. Specifically, a Frequency Decomposition Fusion Enhancement (FDE) strategy first splits the features into low- and high-frequency components and then applies spatial-frequency gating and interactive enhancement to refine the decomposed features. A Mamba-based module is then integrated into the low-frequency branch to model long-range spatial dependencies. Meanwhile, a Multi-Level Feature Aggregation Module (MLFA) leverages multi-level depthwise convolutions and gated aggregation to capture complex multi-level interactions in high-frequency features. Finally, an adaptive frequency fusion (AFF) module dynamically reintegrates these features, yielding a discriminative spectral–spatial representation that integrates global semantics and local textures. Extensive experiments on five benchmark HSI datasets demonstrate that FDM-Net consistently surpasses state-of-the-art methods, achieving the highest OA and Kappa across all five datasets and the best AA on QHUP (92.35%) and QHUT (93.86%). Notably, FDM-Net outperforms the second-best method by margins of 0.28–1.01% in OA and 0.33–1.14% in Kappa.

1. Introduction

Hyperspectral images (HSIs) have become an important source in geoscience and remote sensing (RS) due to their ability to capture detailed spectral signatures of ground objects. Compared with conventional remote sensing imagery, HSIs provide hundreds of contiguous spectral bands together with spatial information, enabling fine-grained material discrimination at the pixel level. Consequently, hyperspectral image classification has become a fundamental task, as accurate land-cover mapping supports many practical applications, including military surveillance, urban planning, and environmental monitoring [1,2].

Numerous methods have been proposed for hyperspectral image classification, evolving from convolutional neural networks (CNNs) to Transformers and more recently to state space models (SSMs) such as Mamba. CNNs provide efficient spectral–spatial feature extraction with low computational cost through weight sharing. For example, Chen et al. [3] proposed the 3D CNN framework for HSI classification, verifying CNNs’ core capability of local spectral–spatial pattern learning. Paoletti et al. [4] proposed a deep pyramidal residual network for hyperspectral image classification, which enhances spectral–spatial feature extraction through residual learning and hierarchical channel expansion. Wang et al. [5] proposed NL2Net, which couples non-local and local feature modeling via a dual-branch architecture to capture both local spatial–spectral structures and long-range dependencies.

Recently, Transformers have been introduced to mitigate the limited receptive field of CNNs by modeling global spectral–spatial dependencies via self-attention. For instance, Hong et al. [6] developed SpectralFormer, which leverages Transformer architecture to capture global spectral–spatial dependencies via sequential band modeling. Sun et al. [7] further introduced a spectral–spatial feature tokenization Transformer, enabling more effective global representation learning. However, Transformers are limited by their high computational cost, as their processing requirements grow exponentially with the size of the input data.

In recent studies, the Mamba model [8] has emerged as a computationally efficient alternative to Transformers, particularly for high-resolution HSI processing. By leveraging the selective state space model (SSM) framework [8], Mamba achieves near-linear complexity with respect to input sequence length while maintaining robust global modeling capabilities. Zhu et al. [9] further extended the selective scanning mechanism to vision tasks. This advancement has recently motivated the development of hybrid CNN–Mamba architectures that integrate the local inductive bias of CNNs with the global dependency modeling capability of Mamba. For example, TinyVim [10] uses CNNs for local feature extraction while employing Mamba for global dependency modeling.

Despite these improvements, several limitations remain in hyperspectral image classification. Moreover, conventional hybrid frameworks typically feed homogeneous features into both branches, failing to rectify the frequency-specific biases of CNNs and Mamba. Since Mamba favors low-frequency global modeling while CNNs focus on high-frequency textures, such uniform processing results in significant feature interference and redundant representations. Furthermore, existing frequency-aware methods often adopt static decomposition with unidirectional information flow, limiting their adaptability to diverse scene characteristics. For instance, DFTN [11] separates frequency components via a fixed FFT-based filter, while WaveFormer [12] employs a static Haar wavelet transform; in both cases, the decomposition is predetermined and the two frequency bands cannot exchange complementary information. In addition, existing CNNs often focus on low- or high-order correlations, failing to exploit the complex multi-level interactions among spectral–spatial features. Specifically, low-order interactions mainly capture simple local patterns, whereas high-order interactions tend to model complex global relationships. The existing network structures are implicitly biased toward low- or high-order feature interactions, ignoring the utilization of multi-level information components.

To address these issues, a Multi-Level Aggregation Network based on Frequency Decomposition (FDM-Net) is proposed. To overcome the frequency-specific bias of homogeneous feature feeding, the framework employs an explicit Frequency Decomposition strategy that routes low-frequency features to a Mamba-based branch for global context modeling and high-frequency features to a dedicated CNN branch for spatial detail extraction, thereby eliminating feature interference. Furthermore, unlike static decomposition with unidirectional information flow, the proposed Frequency Decomposition Fusion Enhancement (FDE) strategy introduces input-adaptive multi-level Gaussian filtering with learnable gating and cross-frequency residual enhancement, enabling bidirectional complementary information exchange between frequency bands. In addition, to address the underutilization of multi-level spatial interactions, a Multi-Level Feature Aggregation Module (MLFA) is introduced in the high-frequency branch, which aggregates local and dilated depthwise convolution responses and modulates them through a gating path, capturing complex spatial correlations beyond single-order interactions. Finally, the two branches are fused through an adaptive frequency fusion module, enabling FDM-Net to achieve competitive performance on hyperspectral image classification. Ablation experiments in Section 4.6 confirm that the FDE strategy alone yields consistent OA gains across datasets (0.17–1.09%), with larger contributions on spectrally complex scenes such as QHUP and Houston. The contributions of this paper are summarized as follows:

1.

A novel multi-level Aggregation Network based on Frequency Decomposition is proposed for hyperspectral image classification. Rather than feeding the same mixed-frequency representation to parallel branches, the framework employs a Frequency Decomposition Fusion Enhancement (FDE) strategy to explicitly separate features: low-frequency structural features are routed to a Mamba-based module for modeling global contextual dependencies, while high-frequency detail features are directed to a dedicated convolutional branch to capture fine-grained spatial information. The dominant features of both branches are subsequently integrated through an adaptive frequency fusion (AFF) module, promoting complementary modeling of global context and local spatial details.

2.

Unlike prior methods that rely on static bases and uniform, data-agnostic separation, FDE introduces input-adaptive multi-level Gaussian filtering with learnable gating, integrated with input-dependent channel–spatial calibration and shared cross-frequency residual enhancement. This enables the network to autonomously determine the optimal frequency partition for each input scene, rather than imposing a fixed, one-size-fits-all decomposition. Before branch-specific modeling, the strategy adaptively recalibrates the decomposed frequency responses and compensates for information loss caused by strict frequency separation, yielding a dynamic, scene-aware separation that respects the unique spectral characteristics of each image.

3.

A Multi-Level Feature Aggregation module is introduced in the high-frequency branch to preserve fine-grained spatial structures. This module aggregates multi-scale spatial responses via local and dilated depthwise separable convolutions, adaptively modulates them through a gating path, and achieves effective channel interaction through feature concatenation and nonlinear fusion. As a result, boundary and texture representation are enhanced while maintaining moderate computational complexity.

2. Related Work

2.1. Frequency-Driven Modeling for HSI Classification

Frequency Decomposition has served as an effective paradigm to disentangle heterogeneous feature semantics within visual data. Low-frequency components dominate global structural trends and smooth spectral responses across ground objects, whereas high-frequency signals encode subtle edges, textural variations and locally distinctive spectral signatures that determine inter-class separability [13]. Early hyperspectral analysis relied on wavelet and Fourier transforms for frequency-domain denoising and band reduction; these traditional tools operated solely on raw pixel spectra without deep feature learning, limiting their capacity to extract hierarchical spatial–spectral representations [14].

Recent studies have demonstrated that frequency-aware representation learning can effectively improve hyperspectral image classification by explicitly separating low-frequency contextual information and high-frequency discriminative details [15]. Building upon this idea, several frequency-driven modeling approaches have been proposed for hyperspectral image classification. Fan et al. [16] introduced a Frequency and Topology Interaction Network (FTIN), which integrates frequency-domain representation learning with topology-aware dependency modeling to enhance spectral–spatial feature discrimination. Cheng et al. [17] proposed SAFDNet, which combines stochastic adaptive Fourier decomposition with CNNs to implement unsupervised feature extraction, lowering network parameters and adapting to scenarios with limited labeled data. Wan et al. [18] designed the dual-branch SSFNet, which decomposes spatial–spectral signals into frequency components and fuses features via gating units and attention modules. Qiao et al. [11] constructed the dual-frequency Transformer DFTN, utilizing neighborhood attention and global filtering to mine high- and low-frequency information. Xi et al. [19] proposed a wide and deep Fourier network (WD-FNet) for HSI classification, leveraging FFT-based sliding-window frequency feature extraction with pruning and a least-squares classifier.

Nevertheless, most existing approaches still employ homogeneous backbone architectures for both low- and high-frequency components, overlooking their inherently distinct representation characteristics. Furthermore, cross-frequency communication is typically restricted to simple fusion operations or attention weighting, lacking dedicated bidirectional interaction pathways capable of fully exploiting complementary frequency cues [20].

2.2. Mamba-Based Dependency Modeling for HSI Classification

Transformers dominated global context modeling for hyperspectral imagery via self-attention, yet their quadratic computational cost hindered deployment on high-dimensional HSI cubes [6]. State space models (SSMs), epitomized by Mamba [8], resolve this bottleneck through linear-complexity selective scanning, dynamically modulating hidden state propagation according to input content rather than computing pairwise token correlations. This efficiency makes Mamba naturally suited for modeling extended spectral in HSI data.

The recent literature has demonstrated the strong capability of Mamba in hyperspectral image classification tasks, particularly in modeling long-range spectral–spatial dependencies with high computational efficiency. Liao et al. [21] proposed a novel hyperspectral image classification method that integrates state space modeling with adaptive recalibration mechanisms, while Zeng et al. [22] demonstrated BioLiteNet to substantially reduce model parameters and computational complexity while maintaining high classification accuracy. Additionally, MambaHSI [23] built disjoint spatial and spectral Mamba blocks to capture cross-dimension long-range interactions, while its upgraded variant MambaHSI+ [24] boosted feature propagation via multi-directional scanning paths. S²Mamba [25] combined structured spatial–spectral traversal with adaptive gating to refine fine-grained sequence embeddings, and SpectralMamba [26] incorporated positional encoding to stabilize spectral sequence modeling.

Despite their strong performance, existing Mamba-centric architectures generally process undifferentiated mixed-frequency feature representations. Owing to its selective state space mechanism and inherent low-pass tendency, Mamba is more effective in modeling low-frequency global structures [10]. In contrast, high-frequency components embedded in the same representation are not sufficiently emphasized, leading to suboptimal utilization of fine-grained discriminative details.

2.3. Hybrid CNN–Mamba Architectures for HSI Classification

Convolutional neural networks (CNNs) have long been a fundamental backbone for hyperspectral image analysis due to their strong capability in capturing local spatial patterns and modeling short-range dependencies. However, their inherently local receptive field limits their ability to effectively model long-range spectral–spatial relationships, which are crucial for complex scene understanding in hyperspectral images. Recently, Mamba-based state space models have emerged as an efficient alternative for long-range dependency modeling. By leveraging selective state space mechanisms, Mamba demonstrates strong capability in capturing global contextual information with linear computational complexity, making it well-suited for modeling long-range spectral–spatial interactions. Nevertheless, its sequence-based formulation tends to prioritize globally smooth structures, which may limit its sensitivity to fine-grained local spatial details.

To address the complementary strengths and limitations of CNNs and Mamba, several hybrid CNN–Mamba architectures have been proposed for hyperspectral image classification. For example, TinyViM [10] adopts a serial design where CNN-based feature extraction is followed by Mamba-based global modeling. DualMamba [27] introduces a parallel dual-branch structure that separately models local spatial features using CNNs and global dependencies using Mamba, and fuses them for final prediction. The SSM-CNN framework [28] uses bidirectional SSM to capture global spectral correlations and shared CNN residual modules to extract spatial features for multisource remote sensing data. It optimizes feature screening via batch normalization and spatial attention and realizes dynamic feature fusion with weighted strategies.

These methods demonstrate the effectiveness of combining convolution-based local modeling with mamba-based modeling. However, they typically operate on mixed spectral–spatial representations without explicitly disentangling low-frequency semantic information from high-frequency structural details. As a result, the complementary strengths of CNNs and Mamba may not be fully exploited, leading to suboptimal utilization of frequency-specific features.

3. Proposed Methodology

Hyperspectral images (HSIs) inherently exhibit multi-frequency characteristics: low-frequency components carry the main structural information and global spectral correlation of ground objects, while high-frequency components contain fine spatial details and discriminative local spectral variations. To fully exploit the complementary information of different frequency components, this paper proposes a frequency-aware dual-branch network named FDM-Net for HSI classification.

As illustrated in Figure 1, the overall pipeline of FDM-Net follows a four-stage architecture: shallow feature embedding, Frequency Decomposition and enhancement, dual-branch feature extraction, and adaptive fusion classification. First, the input HSI patch with size $C\times H\times W$ is fed into a shallow convolutional embedding module to extract primary spatial–spectral features. Then, the Frequency Decomposition Fusion Enhancement (FDE) strategy decomposes the embedded features into low-frequency structural components and high-frequency detail components via multi-level Gaussian filtering, and further enhances the two components through spatial attention and cross-frequency interaction. Afterwards, two parallel branches perform targeted feature modeling on the frequency components respectively: the low-frequency branch adopts a Mamba-based state space model to capture long-range global dependencies, while the high-frequency branch leverages the Multi-Level Feature Aggregation (MLFA) module to mine multi-level local spatial details. Finally, the complementary features from the two branches are dynamically fused by an adaptive frequency fusion module, and fed into the classification head to output pixel-level classification results.

Before Frequency Decomposition, a shallow convolutional embedding module is introduced to perform preliminary spatial–spectral feature extraction on the input HSI patch. The module consists of two stacked $3\times 3$ convolutional layers, each followed by batch normalization (BN) and ReLU activation function. The two convolutional layers maintain the spatial size and channel number of the input feature map and effectively capture local neighborhood spectral–spatial correlations while preserving the original frequency distribution of the input, providing reliable feature basis for subsequent Frequency Decomposition. The calculation process can be expressed as follows:

$${\mathbf{X}}_{embed}={\mathrm{Conv}}_2\left(\mathrm{BN}\left(\mathrm{ReLU}\left({\mathrm{Conv}}_1\left({\mathbf{X}}_{in}\right)\right)\right)\right)$$

(1)

where ${\mathbf{X}}_{in}\in {\mathbb{R}}^{C\times H\times W}$ denotes the input HSI patch, and ${\mathbf{X}}_{embed}$ is the embedded feature output.

3.1. Frequency Decomposition Fusion Enhancement Strategy

To enable each branch to specialize in its corresponding frequency domain, a Frequency Decomposition Fusion Enhancement (FDE) strategy is designed. The strategy decomposes input features into low-frequency and high-frequency components via multi-level Gaussian filtering and introduces adaptive spatial attention and cross-frequency enhancement mechanisms to achieve content-aware frequency separation and complementary information interaction.

First, multi-level Gaussian kernels with different smoothing degrees are constructed to extract low-frequency components at different granularities. The normalized 2D Gaussian kernel with kernel size k and standard deviation $\sigma$ is defined as

$${\mathbf{G}}_k\left(\sigma \right)={\displaystyle \frac{exp\left(-{\displaystyle \frac{x^2+y^2}{2{\sigma }^2}}\right)}{{\sum }_{i,j}exp\left(-{\displaystyle \frac{i^2+j^2}{2{\sigma }^2}}\right)}}$$

(2)

where $(x,y)$ denotes the spatial coordinate relative to the kernel center, and the denominator sums over all positions $(i,j)$ within the $k\times k$ kernel for normalization.

Based on the Gaussian kernels, multi-level low-frequency representations are extracted through depthwise convolution, where each channel is independently filtered to avoid inter-channel information interference. Three kernel sizes of $3\times 3$, $5\times 5$ and $7\times 7$ are adopted, with corresponding standard deviations of $0.8$, $1.5$ and $2.5$, respectively. The convolution process is formulated as

$${\mathbf{F}}_k={\mathbf{X}}_{embed}\mathsf{\ast }{\mathbf{G}}_k\left({\sigma }_k\right),k\in \{3,5,7\}$$

(3)

where $\mathsf{\ast }$ denotes depthwise convolution operation.

The multi-level low-frequency features are fused by weighted summation to obtain the base low-frequency representation, with weights (w) set to 0.5, 0.3 and 0.2, corresponding to the three scales from fine to coarse. The base high-frequency component is obtained by subtracting the low-frequency component from the original embedded feature:

$${\mathbf{Low}}_{base}=0.5·{\mathbf{F}}_3+0.3·{\mathbf{F}}_5+0.2·{\mathbf{F}}_7$$

(4)

$${\mathbf{High}}_{base}={\mathbf{X}}_{embed}-{\mathbf{Low}}_{base}$$

(5)

To achieve content-aware frequency separation, two parallel attention mechanisms are introduced from both channel and spatial dimensions to dynamically weight the frequency components. On the channel dimension, a global adaptive predictor is constructed via global average pooling (GAP) and two point-wise convolutional layers, which predicts three global parameters, low-frequency strength $s_{low}$, high-frequency strength $s_{high}$, and mixing coefficient $\alpha$, to adjust the overall intensity of the two frequency components adaptively according to the input spectral characteristics. On the spatial dimension, a lightweight spatial attention module generates two complementary spatial attention masks ${\mathit{\sigma }}_{low}$ and ${\mathit{\sigma }}_{high}$ through two convolutional layers followed by Softmax normalization along the channel dimension, enabling pixel-level adaptive weighting of frequency components. The calculation is as follows:

$$[{\mathit{\sigma }}_{low},{\mathit{\sigma }}_{high}]=\mathrm{Softmax}\left({\mathrm{Conv}}_{spatial}\left({\mathbf{X}}_{embed}\right)\right)$$

(6)

The attention-weighted frequency features are then obtained by multiplying the base components with channel strength and spatial attention mask simultaneously:

$${\tilde{\mathbf{F}}}_{low}={\mathbf{Low}}_{base}·s_{low}·{\mathit{\sigma }}_{low}$$

(7)

$${\tilde{\mathbf{F}}}_{high}={\mathbf{High}}_{base}·s_{high}·{\mathit{\sigma }}_{high}$$

(8)

To realize cross-frequency information complementation, a shared enhancement feature ${\mathbf{f}}_e$ is generated by concatenating the two weighted frequency features and processing them through a Conv-BN-ReLU module:

$${\mathbf{f}}_e={\mathrm{Conv}}_{1\times 1}\left(\mathrm{BN}\left(\mathrm{ReLU}\left({\mathrm{Conv}}_{1\times 1}\left([{\tilde{\mathbf{F}}}_{low},{\tilde{\mathbf{F}}}_{high}]\right)\right)\right)\right)$$

(9)

where $[·,·]$ denotes channel-wise concatenation along the channel dimension, and ${\mathrm{Conv}}_{1\times 1}$ is a $1\times 1$ convolutional layer that reduces the concatenated channels back to the original dimension. The enhancement feature is then adaptively distributed back to the two branches according to the mixing coefficient $\alpha$:

$${\mathbf{F}}_{low}^{pre}={\tilde{\mathbf{F}}}_{low}+\alpha ·{\mathbf{f}}_e$$

(10)

$${\mathbf{F}}_{high}^{pre}={\tilde{\mathbf{F}}}_{high}+(1-\alpha )·{\mathbf{f}}_e$$

(11)

Furthermore, multi-level residual connections are introduced to stabilize training and avoid information loss during Frequency Decomposition. First, the concatenated dual-branch features are processed by an additional fusion convolution to generate fusion residual features, which are injected into the two frequency branches with a scaling factor of 0.2. Second, the original embedded features are added to both branches with a small scaling factor as global residual connections. The final output frequency features of the FDE module are

$${\mathbf{F}}_{low}={\mathbf{F}}_{low}^{pre}+0.2·{\mathbf{F}}_{fusion}+0.1·{\mathbf{X}}_{embed}$$

(12)

$${\mathbf{F}}_{high}={\mathbf{F}}_{high}^{pre}+0.2·{\mathbf{F}}_{fusion}+0.1·{\mathbf{X}}_{embed}$$

(13)

where ${\mathbf{F}}_{fusion}$ denotes the fusion residual feature. The two frequency features are subsequently fed into the Mamba-based low-frequency branch and MLFA-based high-frequency branch, respectively.

3.2. Multi-Level Feature Aggregation Module (MLFA)

To effectively model multi-level spatial dependencies in high-frequency hyperspectral features and enhance detailed representation, we propose a Multi-Level Feature Aggregation (MLFA) module. As illustrated in Figure 2, the core of the module adopts a dual-path gating design composed of a Value Path $\mathbf{v}$ and a Gate Path $\mathbf{g}$, enabling adaptive enhancement and filtering of multi-level spatial features. The entire MLFA block is built upon a PreNorm residual architecture, integrating a multi-level dilated depthwise convolution unit for multi-level spatial feature extraction and a channel aggregation structure for output feature dimension adjustment.

Given the high-frequency input feature ${\mathbf{F}}_{high}\in {\mathbb{R}}^{B\times C\times H\times W}$, it first undergoes layer normalization under the PreNorm mechanism and then is fed into the dual-path core computing unit.

3.2.1. Value Path

The Value Path extracts multi-level spatial feature representations via hierarchical dilated depthwise convolutions. First, the normalized input passes through a 5 × 5 depthwise convolution with dilation rate $d=1$ to obtain base spatial features:

$${\mathbf{x}}_0={\mathrm{DWConv}}_{5\times 5,d=1}\left(\mathrm{Norm}\left({\mathbf{F}}_{high}\right)\right)$$

(14)

On this basis, two parallel 5 × 5 depthwise convolutions with dilation rate $d=2$ are adopted to augment the contextual receptive field for high-frequency feature extraction, yielding multi-level spatial representations that balance local detail and moderate spatial context:

$${\mathbf{x}}_1={\mathrm{DWConv}}_{5\times 5,d=2}\left({\mathbf{x}}_0\right),{\mathbf{x}}_2={\mathrm{DWConv}}_{5\times 5,d=2}\left({\mathbf{x}}_0\right)$$

(15)

The base feature and two sets of dilated convolution features are concatenated along the channel dimension and then undergo channel transformation and nonlinear activation via a 1 × 1 convolution and SiLU function:

$$\mathbf{v}=\mathrm{SiLU}\left({\mathrm{Conv}}_{1\times 1}\left({\mathbf{x}}_0\parallel {\mathbf{x}}_1\parallel {\mathbf{x}}_2\right)\right)$$

(16)

where $\parallel$ denotes the channel-wise concatenation operation, and $\mathrm{SiLU}\left(x\right)=x·\sigma \left(x\right)$ is the Sigmoid Linear Unit activation function that provides smooth, non-monotonic nonlinearity with self-gating properties.

3.2.2. Gate Path

Parallel to the Value Path, the Gate Path directly generates spatial importance weight signals from the normalized input to realize adaptive modulation of features in the Value Path:

$$\mathbf{g}=\mathrm{SiLU}\left({\mathrm{Conv}}_{1\times 1}\left(\mathrm{Norm}\left({\mathbf{F}}_{high}\right)\right)\right)$$

(17)

The gate weights encode the importance of each spatial position in the feature map, which can selectively enhance the response of discriminative detail regions and suppress redundant noise and invalid responses.

3.2.3. Gated Aggregation and Residual Output

After obtaining the outputs of the two paths, element-wise multiplication is performed between the Value Path features and gate weights to complete gated feature enhancement. Finally, a 1 × 1 aggregation convolution is applied to adjust the channel dimension and output the enhanced high-frequency features:

$${\mathbf{F}}_{high}^{\prime }={\mathrm{Conv}}_{1\times 1}\left(\mathbf{g}\odot \mathbf{v}\right)$$

(18)

where ⊙ denotes the element-wise multiplication operation.

The entire MLFA module adopts a PreNorm residual connection structure. The output of the core gating unit is added with the original input to form a residual path, which ensures stable network training while preserving the original high-frequency information:

$${\mathbf{F}}_{high}^{out}={\mathbf{F}}_{high}+{\mathbf{F}}_{high}^{\prime }$$

(19)

3.3. Mamba-Based Low-Frequency Feature Processing Branch

As illustrated in Figure 1, the low-frequency branch is built upon the Mamba to model long-range global dependencies of low-frequency features with linear computational complexity. The overall pipeline consists of FC embedding, adaptive parameter projection (branches A, B, C, D), and recurrent state space computation.

Given the input low-frequency feature ${\mathbf{F}}_{low}\in {\mathbb{R}}^{B\times C\times H\times W}$ (where B is batch size, C is the number of channels, and $H,W$ denote spatial height and width), we first flatten the 2D spatial feature into a 1D sequence and perform FC embedding via point-wise convolution, obtaining the embedded input sequence:

$$\mathbf{X}=[{\mathbf{x}}_1,{\mathbf{x}}_2,\dots ,{\mathbf{x}}_L],{\mathbf{x}}_t\in {\mathbb{R}}^D$$

(20)

where $L=H\times W$ denotes the total sequence length, and D is the embedding dimension after channel adaptation.

As marked by the four branches (A, B, C, D) in the figure, four independent linear projections are applied to the embedded sequence to generate input-dependent state space parameters. For the t-th token in the sequence, we first compute the discretized state transition matrix ${\overline{\mathbf{A}}}_t$ and input matrix ${\overline{\mathbf{B}}}_t$ from branches A and B, following the selective discretization rule:

$${\overline{\mathbf{A}}}_t=exp({\Delta }_t\odot \mathbf{A}),{\overline{\mathbf{B}}}_t={\Delta }_t\odot \mathbf{B}$$

(21)

where $\mathbf{A}\in {\mathbb{R}}^{d_{state}\times d_{state}}$ and $\mathbf{B}\in {\mathbb{R}}^{d_{state}\times D}$ are learnable base parameters of the state space model; ${\Delta }_t$ is the input-adaptive time step that controls the state update rate, and ⊙ denotes element-wise multiplication.

Based on the discretized parameters, we perform recurrent hidden state update along the sequence direction:

$${\mathbf{h}}_t={\overline{\mathbf{A}}}_t{\mathbf{h}}_{t-1}+{\overline{\mathbf{B}}}_t{\mathbf{x}}_t$$

(22)

where ${\mathbf{h}}_{t-1}\in {\mathbb{R}}^{d_{state}}$ is the hidden state from the previous position, and $d_{state}$ is the dimension of the state space.

Combined with the projection outputs from branches C and D, the output feature at position t is calculated as

$${\mathbf{y}}_t=\mathbf{C}{\mathbf{h}}_t+\mathbf{D}{\mathbf{x}}_t$$

(23)

where $\mathbf{C}\in {\mathbb{R}}^{D\times d_{state}}$ and $\mathbf{D}\in {\mathbb{R}}^D$ are learnable output projection parameters.

Finally, outputs of all positions are concatenated to form the complete output sequence of the low-frequency branch:

$$\mathbf{y}=[{\mathbf{y}}_1,{\mathbf{y}}_2,\dots ,{\mathbf{y}}_L]$$

(24)

The output sequence is reshaped back to a 2D spatial tensor for the subsequent frequency fusion operation.

3.4. Adaptive Frequency Fusion Module

The low-frequency branch extracts global structural features, while the high-frequency branch captures local detail features. The two types of features have strong complementarity. To fully fuse the dual-branch information and dynamically adjust the fusion weight according to input characteristics, this paper designs an adaptive frequency fusion module, which performs adaptive weighted fusion from both channel and spatial dimensions.

First, feature alignment is performed on the dual-branch outputs. Since the channel numbers of the two branches may be different, a point-wise convolution is applied to the high-frequency feature to map its channel number to be consistent with the low-frequency feature. If the spatial sizes of the two features do not match, bilinear interpolation is adopted for upsampling alignment to ensure that the two features can be fused element-wise.

The aligned low-frequency feature ${\mathbf{F}}_{low}^{\prime }$ and high-frequency feature ${\mathbf{F}}_{high}^{\prime }$ are then input into the dual-attention fusion unit. On the channel dimension, global average pooling and global max pooling are performed on each feature respectively to aggregate global spatial information. The pooled features are fed into a shared multi-layer perceptron (MLP) to generate channel attention weights, which are used to weight the importance of each channel adaptively. On the spatial dimension, the channel mean and channel maximum of the two features are concatenated along the channel dimension, and a convolutional layer is applied to generate a spatial attention map, which dynamically weights the importance of different spatial positions.

The weighted features of the two branches are added element-wise to obtain the final fused feature ${\mathbf{F}}_{fuse}$:

$${\mathbf{F}}_{fuse}=\left({\mathbf{M}}_c^{low}\odot {\mathbf{M}}_s^{low}\odot {\mathbf{F}}_{low}^{\prime }\right)+\left({\mathbf{M}}_c^{high}\odot {\mathbf{M}}_s^{high}\odot {\mathbf{F}}_{high}^{\prime }\right)$$

(25)

where ${\mathbf{M}}_c\in {\mathbb{R}}^{C\times 1\times 1}$ and ${\mathbf{M}}_s\in {\mathbb{R}}^{1\times H\times W}$ denote the channel attention weight and spatial attention weight respectively. This adaptive fusion mechanism can dynamically adjust the fusion ratio of structural information and detail information according to the characteristics of input samples, effectively integrating the advantages of dual-branch features and improving the discriminative ability of the fused features.

3.5. Classification Head and Loss Function

The fused feature is first fed into a global average pooling layer to compress the 2D spatial feature into a channel-wise feature vector, which reduces the number of parameters and preserves global semantic information. Then, a dropout layer with a dropout rate of 0.3 is applied to alleviate overfitting. Finally, the feature vector is mapped to the class dimension through a fully connected layer, and the classification probability is obtained after Softmax normalization.

The network is trained end-to-end with the cross-entropy loss function, which is defined as

$${\mathcal{L}}_{ce}=-{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}{\displaystyle \sum _{k=1}^K}{y}_{i,k}log{\hat{y}}_{i,k}$$

(26)

where N is the number of samples in a batch, K is the total number of categories, $y_{i,k}$ is the one-hot encoded ground truth label of the i-th sample for the k-th category, and ${\hat{y}}_{i,k}$ is the corresponding predicted probability.

4. Experiment Results and Analysis

4.1. Datasets

(1)

QUH-Pingan (QUHP): The QUH-Pingan dataset [14] was acquired from 10:43 to 11:28 on 19 May 2021, over the Huangdao Pingan Passenger Ship Terminal in Qingdao, China. The UAV flew at an altitude of 200 m, yielding a spatial resolution of 0.10 m. The imagery has a spatial size of $1230\times 1000$ pixels and covers 176 spectral bands in the wavelength range of 400–1000 nm. It contains 10 land-cover classes, including Ship, Seawater, Trees, Concrete structure building, Floating pier, Brick houses, Steel houses, Wharf construction land, Car, and Road, with large-scale variation: large-scale (Seawater, Road), medium-scale (Trees, Floating pier, Brick houses, Steel houses), and small-scale (Ship, Car) targets, where the latter are the most difficult to identify. Following the spatially disjoint protocol, 1% of the labeled samples per class were used for training, with the remaining samples reserved for testing.

(2)

QUH-Qingyun (QUHQ): The QUH-Qingyun dataset [14] was collected from 14:06 to 14:45 on 18 May 2021, over a residential and primary school area on Qingyun Road, Qingdao, China, at an altitude of 300 m with a spatial resolution of 0.15 m. The image size is $880\times 1360$ pixels, covering 270 spectral bands from 400 to 1000 nm. It comprises six land-cover classes: Trees, Concrete building, Car, Ironhide building, Plastic playground, and Asphalt road. A key challenge of this dataset lies in shadow occlusion (affecting Trees, Car, and Asphalt road) and the recognition of small-scale targets (e.g., Car), which can significantly reduce classification accuracy and robustness. Under the spatially disjoint protocol, 1% of the labeled samples per class were used for training.

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QUH-Tangdaowan (QUHT): The QUH-Tangdaowan dataset [14] was acquired from 11:23 to 12:05 on 18 May 2021, over Tangdao Bay National Wetland Park in Qingdao, China, at a flight altitude of 300 m with a spatial resolution of 0.15 m. The data has a spatial size of $1740\times 860$ pixels and spans 176 spectral bands in the range of 400–1000 nm. It is the most complex of the three QUH sub-datasets, containing 18 land-cover classes with high intra-class spectral similarity—notably four vegetation species (Coniferous pine, Buxus sinica, Populus, Ulmus pumila L.) and three pavement types (Flagging, Boardwalk, Gravel road) that are spectrally nearly indistinguishable, posing a significant challenge for precise classification. Following the spatially disjoint protocol, 1% of the labeled samples per class were used for training.

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Houston: The Houston dataset [29] was collected in June 2012 via the ITRES CASI-1500 airborne sensor over the University of Houston campus and the neighboring urban area and was officially released for the 2013 IEEE GRSS Data Fusion Contest. The image has a spatial size of $349\times 1905$ pixels with a spatial resolution of 2.5 m, covering 144 spectral bands in the wavelength range of 380–1050 nm. It contains 15 urban land-cover classes, including Healthy grass, Stressed grass, Synthetic grass, Tree, Soil, Water, Residential, Commercial, Road, Highway, Railway, Parking lot 1, Parking lot 2, Tennis court, and Running track, with a total of 15,029 labeled samples (2832 for training and 12,197 for testing) under complex urban illumination conditions. In our experiments, 2% of the labeled samples from each class were randomly selected for training, with the remaining samples reserved for testing.

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Indian Pines (IP): The Indian Pines dataset [30] was acquired in 1992 via the AVIRIS (Airborne Visible/Infrared Imaging Spectrometer) sensor over an agricultural and forested test site in Northwestern Indiana, USA. The image consists of $145\times 145$ pixels with a spatial resolution of 20 m, spanning 220 spectral bands in the wavelength range of 400–2500 nm. After removing 24 water-absorption and noisy bands (bands 104–108, 150–163, and 220), 200 spectral bands were retained for experiments. The dataset contains 16 land-cover classes with a total of 10,249 labeled samples, covering a variety of agricultural categories such as Corn-notill (1428 samples), Soybean-mintill (2455 samples), and minority classes such as Alfalfa (46 samples) and Oats (20 samples), resulting in a highly imbalanced class distribution that poses significant classification challenges. In this study, 10% of the labeled samples from each class were randomly selected for training, and the remaining 90% were reserved for evaluation.

4.2. Experimental Settings

All experiments were conducted on a single NVIDIA RTX 5060 GPU using PyTorch 2.7.0. The model was trained for 300 epochs with a batch size of 32, using the AdamW optimizer ($lr=1\times {10}^{-4}$) and a cosine learning rate scheduler, and three widely used metrics in hyperspectral image classification were adopted: Overall Accuracy (OA), Average Accuracy (AA), and the Kappa coefficient ($\kappa$). OA measures the ratio of correctly classified samples to the total number of test samples, AA computes the mean accuracy across all classes, and $\kappa$ evaluates the agreement between predicted labels and ground truth.

4.3. Performance Comparison

To validate the effectiveness of the proposed method, comprehensive experiments were conducted on the five mentioned benchmark datasets. Several state-of-the-art hyperspectral image classification methods were selected as comparison models, including Lite-HCNet [31], LSSAN [32], MSDAN [33], SimPoolFormer [34], SpectralFormer [6], CacfNet [35], GSCViT [36], and SSFTT [7].

(1) Results on QHUP Dataset:

As shown in

Table 1. Class-wise classification accuracies (%) on the QHUP dataset. The best results are shown in bold.

Class	Lite-HCNet	LSSAN	SimPoolFormer	CacfNet	MSDAN	SpectralFormer	GSCViT	SSFTT	Our Method
Class 1	83.86 ± 3.65	90.51 ± 3.17	79.16 ± 5.31	85.68 ± 5.55	88.97 ± 2.47	83.84 ± 1.55	83.20 ± 7.09	84.26 ± 3.24	91.50 ± 4.08
Class 2	99.06 ± 0.26	98.78 ± 0.40	98.98 ± 0.40	99.08 ± 0.34	98.60 ± 0.36	99.01 ± 0.12	99.30 ± 0.39	98.53 ± 0.10	98.88 ± 0.46
Class 3	96.10 ± 2.45	92.75 ± 3.15	85.79 ± 16.58	82.37 ± 14.53	92.09 ± 1.66	94.34 ± 2.26	92.27 ± 3.85	89.38 ± 2.50	94.23 ± 4.86
Class 4	96.42 ± 1.17	93.56 ± 1.03	94.10 ± 3.14	92.63 ± 1.46	94.50 ± 1.69	90.23 ± 1.31	91.09 ± 3.22	85.94 ± 2.06	96.93 ± 0.50
Class 5	87.58 ± 3.17	78.10 ± 3.85	88.32 ± 2.64	76.85 ± 7.29	86.51 ± 4.38	84.75 ± 1.55	78.85 ± 0.45	67.71 ± 5.93	85.49 ± 7.85
Class 6	96.11 ± 1.36	89.03 ± 7.77	90.63 ± 11.05	95.15 ± 1.94	94.18 ± 1.60	89.27 ± 1.58	91.78 ± 0.50	90.54 ± 2.74	95.10 ± 3.39
Class 7	89.96 ± 6.29	91.57 ± 3.01	90.29 ± 3.42	86.20 ± 6.04	90.07 ± 3.09	89.47 ± 2.63	92.36 ± 4.72	83.33 ± 2.17	90.87 ± 3.48
Class 8	96.14 ± 1.44	95.26 ± 0.97	92.86 ± 7.05	92.46 ± 1.62	95.36 ± 2.25	92.05 ± 1.16	94.14 ± 1.00	85.01 ± 1.20	96.99 ± 0.46
Class 9	75.68 ± 8.71	59.98 ± 11.69	63.26 ± 16.13	57.02 ± 19.10	68.63 ± 6.87	53.99 ± 7.77	76.03 ± 2.02	52.35 ± 6.37	75.12 ± 12.07
Class 10	97.41 ± 0.73	97.46 ± 0.38	98.19 ± 1.66	97.17 ± 1.38	97.81 ± 0.34	97.92 ± 0.15	96.70 ± 0.00	94.61 ± 0.70	98.43 ± 0.51
OA (%)	97.04 ± 0.11	96.54 ± 0.19	96.36 ± 0.50	96.03 ± 0.43	96.80 ± 0.18	96.05 ± 0.07	96.18 ± 0.13	93.76 ± 0.06	97.58 ± 0.07
AA (%)	91.83 ± 0.95	88.70 ± 0.90	88.16 ± 2.14	86.46 ± 2.51	90.67 ± 1.39	87.49 ± 0.84	88.49 ± 1.45	83.17 ± 0.19	92.35 ± 0.75
Kappa (%)	95.59 ± 0.16	94.85 ± 0.28	94.55 ± 0.74	94.06 ± 0.64	95.23 ± 0.28	94.10 ± 0.11	94.30 ± 0.21	90.71 ± 0.07	96.39 ± 0.11

, FDM-Net achieves the best overall performance on the QHUP dataset, with an OA of 97.58%, AA of 92.35% and Kappa coefficient of 96.39%, all ranking first among the compared methods. Specifically, compared with the second-best method Lite-HCNet in terms of OA, FDM-Net yields an improvement of 0.54%. For AA and Kappa metrics, it outperforms the runner-up Lite-HCNet by 0.52% and 0.80% respectively, verifying its strong classification capability for complex land-cover scenes. The gains are particularly evident on challenging categories: for spectrally heterogeneous classes with large intra-class variance (e.g., Class 1 and Class 4), FDM-Net attains 91.50% and 96.93% respectively, benefiting from its frequency-adaptive feature decomposition that enhances robustness to intra-class spectral variations. On the most challenging Class 9, which suffers from limited training samples and severe spectral confusion, FDM-Net achieves a competitive 75.12% with higher stability.

Figure 3 presents the classification maps of all methods on the QHUP dataset for visual verification. Most competing methods produce scattered salt-and-pepper misclassification noise in homogeneous ground object regions, with blurred and jagged boundaries between different categories. Especially for methods like LSSAN and CacfNet, misclassification noise is more prominent in fine-grained local regions, and the structural morphology of small ground objects deviates obviously from the ground truth. In contrast, FDM-Net generates classification maps with significantly higher spatial consistency: it effectively suppresses random noise, retains the complete structure of ground objects, and renders smoother and more accurate category boundaries. Its overall visual effect is highly consistent with the ground truth map, which matches the quantitative evaluation conclusions.

(2) Results on QHUQ Dataset: As shown in

Table 2. Class-wise classification accuracies (%) on the QHUQ dataset. The best results are shown in bold.

Class	Lite-HCNet	LSSAN	MSDAN	SimPoolFormer	CacfNet	SpectralFormer	GSCViT	SSFTT	Our Method
Class 1	96.02 ± 0.30	95.42 ± 0.44	94.10 ± 1.22	95.50 ± 0.72	93.17 ± 0.91	94.79 ± 0.33	95.54 ± 1.44	95.89 ± 0.63	96.16 ± 0.50
Class 2	95.03 ± 1.41	96.06 ± 0.26	93.88 ± 2.33	95.46 ± 1.46	95.61 ± 2.26	93.02 ± 1.36	95.04 ± 1.57	95.08 ± 0.98	97.16 ± 0.60
Class 3	51.81 ± 5.48	49.65 ± 2.67	50.64 ± 17.68	53.43 ± 5.50	53.87 ± 11.33	36.92 ± 3.65	55.59 ± 5.51	56.42 ± 5.77	51.10 ± 9.97
Class 4	97.99 ± 0.38	98.08 ± 0.17	97.60 ± 1.77	97.66 ± 0.12	98.06 ± 0.98	97.97 ± 0.12	97.74 ± 1.38	98.86 ± 0.67	97.14 ± 0.44
Class 5	94.89 ± 0.68	95.78 ± 0.42	95.51 ± 1.36	95.35 ± 0.62	95.99 ± 1.02	94.99 ± 0.33	95.94 ± 0.60	95.80 ± 0.26	95.40 ± 0.65
Class 6	93.55 ± 0.82	92.64 ± 1.05	93.89 ± 0.91	93.50 ± 0.62	92.57 ± 2.32	92.02 ± 0.75	93.35 ± 1.64	93.35 ± 0.71	94.44 ± 0.76
OA (%)	94.30 ± 0.10	94.24 ± 0.15	93.59 ± 0.21	93.73 ± 0.61	94.34 ± 0.16	92.95 ± 0.14	94.40 ± 0.14	94.50 ± 0.09	95.07 ± 0.08
AA (%)	88.22 ± 0.88	87.94 ± 0.43	88.21 ± 1.84	87.60 ± 3.33	88.48 ± 0.76	84.95 ± 0.59	88.87 ± 0.87	89.23± 0.95	88.57 ± 1.54
Kappa (%)	92.43 ± 0.13	92.37 ± 0.20	91.52 ± 0.28	91.69 ± 0.82	92.50 ± 0.21	90.65 ± 0.19	92.58 ± 0.18	92.71 ± 0.11	93.47 ± 0.10

, FDM-Net achieves the best OA (95.07%) and Kappa (93.47%) on the QHUQ dataset, with a competitive AA of 88.57%. Compared with CacfNet, it yields a 0.73% OA improvement and a 0.97% Kappa gain. Even for challenging categories with limited training samples and severe spectral confusion (e.g., Class 3), FDM-Net maintains competitive accuracy, verifying its robust classification capability and balanced recognition performance across all land-cover classes. These results demonstrate the effectiveness of the proposed Frequency Decomposition Fusion Enhancement (FDE) strategy in extracting discriminative spectral–spatial representations through explicit Frequency Decomposition and complementary integration of low-frequency and high-frequency components. At the class-wise level, FDM-Net achieves optimal accuracy on three of the six categories (Class 1, Class 2, and Class 6), attaining 96.16%, 97.16%, and 94.44% respectively, which demonstrates the effectiveness of the proposed FDE strategy in extracting discriminative representations for spectrally homogeneous classes.

Figure 4 presents the classification maps of all methods. Most methods produce obvious scattered misclassifications in homogeneous regions, with blurred object boundaries and degraded spatial consistency; LSSAN and SpectralFormer suffer from more misclassified pixels in fine-grained local areas. In contrast, FDM-Net generates classification maps closest to the ground truth: it effectively suppresses isolated noise, preserves the structural integrity of ground objects, and outputs clearer category boundaries. These visual findings align with the quantitative results, which benefit from the collaborative modeling of low-frequency semantic information and high-frequency structural details, achieving both global consistency and local discriminability. The superior preservation of fine-grained spatial structures and sharp boundaries further validates the effectiveness of the MLFA module in capturing multi-level spatial details within the high-frequency branch.

(3) Results on QHUT Dataset: The QHUT dataset poses greater classification challenges due to its abundant land-cover categories and serious spectral overlap between similar ground objects. As recorded in

Table 3. Class-wise classification accuracies (%) on the QHUT dataset. The best results are shown in bold.

Class	Lite-HCNet	LSSAN	MSDAN	SimPoolFormer	CacfNet	SpectralFormer	GSCViT	SSFTT	Our Method
Class 1	98.97 ± 0.33	99.12 ± 0.38	98.94 ± 0.59	99.66 ± 0.34	98.86 ± 0.61	99.45 ± 0.34	99.37 ± 0.73	99.78 ± 0.07	99.84 ± 0.11
Class 2	99.06 ± 0.36	96.12 ± 1.78	97.29 ± 2.08	98.31 ± 1.09	98.19 ± 0.77	98.21 ± 0.90	99.07 ± 0.21	98.35 ± 0.50	99.46 ± 0.22
Class 3	93.53 ± 3.51	94.13 ± 3.29	94.24 ± 4.37	90.86 ± 7.65	94.99 ± 2.70	96.03 ± 1.67	96.94 ± 0.45	93.59 ± 2.23	95.83 ± 1.16
Class 4	98.89 ± 0.71	98.87 ± 0.52	98.80 ± 0.35	98.91 ± 1.05	99.28 ± 0.18	99.20 ± 0.37	98.92 ± 0.49	99.40 ± 0.23	99.71 ± 0.22
Class 5	92.90 ± 2.37	80.16 ± 8.47	84.38 ± 9.25	90.90 ± 6.49	85.07 ± 8.57	23.08 ± 22.80	83.71 ± 9.02	88.89 ± 4.67	92.11 ± 9.27
Class 6	91.80 ± 3.86	86.81 ± 3.63	90.10 ± 4.50	89.07 ± 6.46	95.50 ± 2.55	85.70 ± 3.08	89.11 ± 1.14	91.60 ± 2.34	93.46 ± 1.19
Class 7	81.97 ± 5.46	72.99 ± 4.10	77.75 ± 4.72	82.04 ± 3.07	85.40 ± 3.15	63.32 ± 13.10	81.74 ± 1.80	79.12 ± 4.35	85.64 ± 3.11
Class 8	99.81 ± 0.08	99.63 ± 0.42	98.96 ± 1.09	99.71 ± 0.21	99.86 ± 0.08	99.64 ± 0.06	99.67 ± 0.17	99.70 ± 0.14	99.80 ± 0.14
Class 9	97.96 ± 1.22	98.96 ± 0.36	98.89 ± 1.06	98.66 ± 1.28	99.34 ± 0.65	98.03 ± 1.62	99.02 ± 1.34	99.21 ± 0.36	99.54 ± 0.33
Class 10	82.59 ± 33.80	91.02 ± 5.14	81.06 ± 16.27	91.95 ± 5.52	95.61 ± 2.99	65.85 ± 36.90	94.63 ± 3.97	90.89 ± 3.70	96.65 ± 2.16
Class 11	88.47 ± 3.19	85.65 ± 3.93	79.31 ± 5.12	75.33 ± 8.17	94.97 ± 2.17	80.22 ± 6.80	91.71 ± 3.95	88.41 ± 3.83	94.07 ± 1.84
Class 12	81.67 ± 15.88	60.54 ± 22.30	56.92 ± 34.47	71.85 ± 16.62	42.37 ± 35.97	0.08 ± 0.18	81.24 ± 4.91	78.71 ± 5.69	72.44 ± 22.47
Class 13	98.68 ± 0.28	96.09 ± 2.62	89.45 ± 16.23	83.43 ± 30.22	94.88 ± 2.76	94.26 ± 5.29	99.40 ± 1.08	97.18 ± 1.32	99.53 ± 0.43
Class 14	86.57 ± 6.14	60.69 ± 13.32	78.93 ± 17.04	43.92 ± 40.81	80.02 ± 12.60	10.35 ± 12.53	79.76 ± 16.24	77.45 ± 12.95	79.70 ± 14.49
Class 15	89.00 ± 3.21	83.90 ± 2.57	90.09 ± 2.69	84.35 ± 3.37	92.15 ± 1.32	86.63 ± 3.75	84.51 ± 2.37	85.50 ± 2.17	92.36 ± 2.21
Class 16	95.47 ± 1.30	94.83 ± 0.95	95.31 ± 1.84	95.10 ± 1.25	95.50 ± 1.39	93.35 ± 1.44	96.07 ± 1.23	96.39 ± 0.89	97.88 ± 0.73
Class 17	88.73 ± 6.12	86.66 ± 2.48	88.97 ± 3.84	88.97 ± 1.63	93.16 ± 3.01	87.64 ± 4.66	84.73 ± 5.90	89.38 ± 1.59	91.63 ± 1.74
Class 18	99.64 ± 0.18	99.68 ± 0.33	98.97 ± 0.82	99.68 ± 0.27	99.88 ± 0.09	99.87 ± 0.09	99.92 ± 0.09	99.91 ± 0.07	99.85 ± 0.23
OA (%)	95.99 ± 0.10	94.69 ± 0.14	95.07 ± 0.63	94.83 ± 0.11	96.82 ± 0.20	93.78 ± 0.90	96.19 ± 0.09	96.15 ± 0.05	97.58 ± 0.14
AA (%)	92.54 ± 2.11	88.10 ± 1.17	88.80 ± 2.99	87.93 ± 3.34	91.39 ± 3.15	76.72 ± 5.14	92.20 ± 2.01	91.86 ± 0.78	93.86 ± 0.87
Kappa (%)	95.44 ± 0.12	93.95 ± 0.16	94.38 ± 0.70	94.10 ± 0.13	96.38 ± 0.22	92.91 ± 1.04	95.78 ± 0.23	95.61 ± 0.06	97.25 ± 0.16

, FDM-Net ranks first on OA (97.58%), AA (93.86%) and Kappa (97.25%). Relative to CacfNet, our method gains 0.76% OA and 0.87% Kappa improvements. Many existing algorithms suffer from unstable per-class performance here—for example, SpectralFormer delivers an extremely low AA of 76.72% with a large deviation. In contrast, our frequency-decoupled framework achieves balanced, stable classification across all categories, demonstrating strong robustness against complex spectral interference. Notably, competing methods collapse on the most challenging categories where training samples are extremely limited. For instance, SpectralFormer drops to 0.08% and 10.35% on Class 12 and Class 14, as its Transformer-based architecture suffers from insufficient data for learning discriminative token representations. In contrast, FDM-Net still retains 72.44% and 79.70% on these same categories. Equally telling is the stability gap: competing methods show deviations up to 36.90%, while FDM-Net delivers consistent performance across all categories.

As displayed in Figure 5, fragmented land parcels and numerous linear features such as roads lead to severe structural distortion and widespread misclassification noise for most compared models, and several methods even generate large-scale wrong predictions for spectrally similar land covers. By separately modeling low-frequency global context and high-frequency details, FDM-Net effectively suppresses intra-region noise, maintains the morphological continuity of linear terrain features, and reconstructs precise, smooth classification boundaries, thus delivering the most visually faithful prediction against the ground truth. The notable fidelity in reconstructing fine linear structures and intricate land parcel boundaries further underscores the effectiveness of the MLFA module in preserving detailed spatial information through multi-level feature aggregation within the high-frequency branch.

(4) Results on Houston Dataset:

As a typical urban scene with finely distributed diverse ground objects, the Houston dataset demands strong fine-grained feature discrimination capability. As shown in

Table 4. Class-wise classification accuracies (%) on the Houston dataset. The best results are shown in bold.

Class	Lite-HCNet	LSSAN	MSDAN	SimPoolFormer	CacfNet	SpectralFormer	GSCViT	SSFTT	FDM-Net
Class 1	97.44 ± 0.55	96.54 ± 0.59	95.77 ± 0.74	96.77 ± 0.69	91.66 ± 4.07	96.79 ± 0.72	93.68 ± 1.42	94.67 ± 0.25	97.38 ± 0.29
Class 2	98.13 ± 0.83	97.22 ± 1.73	96.05 ± 1.45	95.51 ± 2.01	91.49 ± 4.35	96.63 ± 1.09	95.87 ± 0.95	95.70 ± 0.32	98.32 ± 0.62
Class 3	99.85 ± 0.10	98.71 ± 1.44	100.00 ± 0.00	97.86 ± 1.65	93.65 ± 1.97	99.27 ± 0.94	97.82 ± 0.33	96.40 ± 0.29	99.84 ± 0.15
Class 4	97.26 ± 1.24	95.57 ± 3.61	95.21 ± 3.03	97.77 ± 1.49	93.31 ± 2.40	98.85 ± 1.70	96.81 ± 0.84	95.54 ± 1.12	99.67 ± 0.36
Class 5	98.95 ± 0.43	99.13 ± 0.86	99.98 ± 0.04	97.72 ± 3.39	97.39 ± 0.82	99.84 ± 0.17	97.77 ± 0.07	97.48 ± 0.24	99.93 ± 0.07
Class 6	97.37 ± 3.15	87.65 ± 5.35	97.05 ± 2.20	89.59 ± 3.34	48.28 ± 13.71	84.58 ± 5.96	93.77 ± 2.32	94.54 ± 3.86	95.77 ± 2.54
Class 7	91.36 ± 0.68	84.83 ± 3.15	89.27 ± 1.14	89.37 ± 5.55	67.00 ± 6.99	88.66 ± 3.11	90.03 ± 3.02	91.47 ± 0.43	93.06 ± 3.03
Class 8	85.09 ± 1.59	76.14 ± 8.66	89.94 ± 2.58	84.48 ± 0.59	66.48 ± 4.97	80.36 ± 4.18	85.90 ± 2.82	82.76 ± 1.44	88.00 ± 2.99
Class 9	87.69 ± 0.58	73.66 ± 6.66	80.69 ± 3.18	83.00 ± 2.36	71.16 ± 6.32	85.17 ± 5.39	85.72 ± 2.48	84.63 ± 2.03	90.57 ± 1.28
Class 10	96.33 ± 1.61	90.74 ± 1.89	93.19 ± 1.88	92.20 ± 1.31	78.85 ± 4.35	96.46 ± 1.42	95.42 ± 1.23	93.57 ± 0.76	96.03 ± 1.05
Class 11	98.02 ± 0.94	93.75 ± 3.33	95.74 ± 2.81	93.97 ± 2.11	71.07 ± 5.42	97.97 ± 1.16	93.82 ± 3.22	94.57 ± 0.96	95.82 ± 1.79
Class 12	94.96 ± 1.79	89.49 ± 5.78	96.21 ± 1.63	91.01 ± 5.98	74.82 ± 10.45	96.01 ± 2.11	95.13 ± 1.32	91.09 ± 2.01	94.52 ± 3.03
Class 13	74.20 ± 7.09	64.82 ± 4.36	81.09 ± 9.04	39.30 ± 19.49	22.56 ± 13.87	44.30 ± 9.52	85.34 ± 7.15	91.72 ± 1.77	68.93 ± 12.14
Class 14	97.85 ± 1.15	88.45 ± 11.72	99.86 ± 0.21	93.32 ± 6.86	87.88 ± 7.63	96.28 ± 6.36	97.51 ± 0.21	96.06 ± 0.57	97.52 ± 2.18
Class 15	99.75 ± 0.28	99.17 ± 1.46	97.16 ± 1.67	99.29 ± 1.59	92.77 ± 1.66	98.86 ± 0.62	97.63 ± 0.38	96.79 ± 1.27	99.20 ± 1.02
OA (%)	94.51 ± 0.35	89.67 ± 1.01	93.56 ± 0.25	91.07 ± 0.77	79.20 ± 2.78	92.48 ± 0.63	93.54 ± 0.13	93.69 ± 0.25	94.79 ± 0.27
AA (%)	94.28 ± 0.56	89.06 ± 1.34	93.80 ± 0.61	89.41 ± 1.37	76.56 ± 2.31	90.67 ± 0.68	93.55 ± 0.24	93.31 ± 0.35	94.24 ± 0.50
Kappa (%)	94.06 ± 0.38	88.83 ± 1.09	93.04 ± 0.27	90.34 ± 0.83	77.48 ± 3.01	91.86 ± 0.69	92.98 ± 0.14	93.18 ± 0.27	94.39 ± 0.27

, FDM-Net ranks first in OA and Kappa (94.79% and 94.39%), and second in AA (94.24%, slightly behind Lite-HCNet at 94.28%). Compared with the runner-up Lite-HCNet, it yields an OA improvement of 0.28% and a Kappa gain of 0.33%. Many compared methods suffer from severe performance degradation in this complex scene—CacfNet, for instance, only achieves an OA of 79.20%. FDM-Net additionally avoids the severe collapses seen in competing methods, while CacfNet and SimPoolFormer fall below 40% on Class 13. For fine-grained urban classes, FDM-Net surpasses competitors by up to 16.91 %, with consistently lower per-class variance, confirming the robustness of the frequency-decoupled design.

The classification maps for visual verification are shown in Figure 6. It is evident that most compared methods suffer from degraded spatial consistency in homogeneous regions, as well as structural fracture and misclassification on narrow linear features such as roads. Some methods even exhibit large-area classification errors on spectrally similar urban objects, which is consistent with their poor quantitative performance. In contrast, FDM-Net produces classification maps that are significantly closer to the ground truth, with markedly clearer boundaries and higher spatial consistency. It effectively preserves the integrity of small urban targets and maintains the morphological continuity of linear features. These visual results confirm the effectiveness of FDM-Net. This advantage stems from the collaborative modeling of high-frequency edge details through the MLFA module and low-frequency global semantics through the FDE strategy, which well accommodates the fine-grained classification demands of complex urban scenarios.

(5) Results on Indian Pines Dataset: The Indian Pines dataset poses severe few-shot classification challenges due to extreme sample imbalance and heavy spectral overlap across various crop types. As summarized in

Table 5. Class-wise classification accuracies (%) on the Indian Pines (IP) dataset. The best results are shown in bold.

Class	Lite-HCNet	LSSAN	MSDAN	SimPoolFormer	CacfNet	SpectralFormer	GSCViT	SSFTT	FDM-Net
Class 1	89.27 ± 12.51	71.71 ± 15.48	49.78 ± 4.04	95.12 ± 4.23	91.27 ± 2.16	93.66 ± 1.34	100.00 ± 0.00	99.02 ± 1.34	96.58 ± 5.35
Class 2	93.01 ± 0.90	85.54 ± 3.11	81.33 ± 4.35	84.08 ± 3.65	94.99 ± 0.39	81.90 ± 4.34	96.00 ± 1.99	94.18 ± 2.15	95.67 ± 1.35
Class 3	98.18 ± 1.26	83.13 ± 3.10	92.27 ± 3.39	83.96 ± 6.45	98.32 ± 1.16	88.49 ± 2.45	98.79 ± 0.93	97.59 ± 0.63	99.04 ± 0.67
Class 4	92.02 ± 7.59	74.08 ± 8.81	88.18 ± 1.61	72.68 ± 12.18	99.28 ± 0.41	69.76 ± 7.93	99.34 ± 0.63	98.78 ± 1.71	98.22 ± 2.26
Class 5	96.27 ± 1.46	90.07 ± 3.32	94.92 ± 3.90	92.23 ± 4.77	98.74 ± 1.35	91.54 ± 1.51	96.69 ± 2.22	97.01 ± 2.09	96.73 ± 0.72
Class 6	98.20 ± 1.47	94.46 ± 2.52	98.87 ± 0.73	97.32 ± 1.89	98.20 ± 0.06	98.36 ± 0.70	98.17 ± 0.51	98.20 ± 0.46	98.42 ± 1.01
Class 7	100.00 ± 0.00	88.80 ± 15.34	97.04 ± 6.62	83.20 ± 17.75	100.00 ± 0.00	84.80 ± 7.16	98.40 ± 3.58	100.00 ± 0.00	88.00 ± 12.45
Class 8	99.11 ± 1.05	98.84 ± 1.25	99.01 ± 0.93	98.14 ± 1.56	97.80 ± 1.23	99.58 ± 0.45	100.00 ± 0.00	98.37 ± 3.64	99.81 ± 0.42
Class 9	42.22 ± 43.50	66.67 ± 6.80	76.84 ± 8.81	45.56 ± 47.53	90.03 ± 9.96	63.33 ± 12.79	77.78 ± 17.12	71.11 ± 24.34	80.00 ± 18.35
Class 10	96.89 ± 1.68	86.99 ± 2.03	92.32 ± 1.89	85.28 ± 6.95	97.64 ± 0.25	90.17 ± 1.11	96.98 ± 2.11	98.79 ± 1.72	97.44 ± 0.59
Class 11	98.71 ± 0.79	96.61 ± 1.26	96.73 ± 0.98	93.84 ± 3.42	98.67 ± 0.20	93.80 ± 0.96	98.83 ± 1.41	99.09 ± 0.88	99.52 ± 0.28
Class 12	92.99 ± 2.27	85.73 ± 4.89	82.02 ± 2.73	82.47 ± 3.18	91.43 ± 0.40	77.64 ± 5.60	94.53 ± 3.76	88.28 ± 6.78	94.94 ± 1.92
Class 13	96.97 ± 2.93	88.76 ± 4.81	83.11 ± 11.21	94.49 ± 5.83	93.22 ± 0.47	98.60 ± 1.24	98.27 ± 2.37	99.57 ± 0.24	98.16 ± 1.82
Class 14	99.54 ± 0.83	96.58 ± 1.10	99.64 ± 0.35	98.98 ± 1.19	99.86 ± 0.31	97.57 ± 1.34	99.73 ± 0.35	99.58 ± 0.48	99.77 ± 0.15
Class 15	97.75 ± 1.91	83.17 ± 5.79	92.25 ± 1.79	88.82 ± 5.80	96.24 ± 0.50	82.65 ± 2.26	97.18 ± 1.65	98.73 ± 1.20	99.65 ± 0.24
Class 16	80.48 ± 14.93	74.53 ± 8.65	74.67 ± 6.87	86.90 ± 10.51	74.26 ± 1.41	89.76 ± 2.17	81.43 ± 3.10	71.19 ± 10.82	88.10 ± 6.43
OA (%)	96.80 ± 0.16	90.50 ± 0.44	92.40 ± 0.60	90.37 ± 1.72	97.22 ± 0.08	90.39 ± 0.73	97.77 ± 0.35	97.18 ± 0.60	98.78 ± 0.17
AA (%)	91.98 ± 3.15	85.35 ± 0.88	87.44 ± 1.26	86.44 ± 4.77	95.81 ± 1.19	87.60 ± 0.73	95.76 ± 0.80	94.34 ± 1.95	94.55 ± 1.98
Kappa (%)	96.35 ± 0.19	89.15 ± 0.52	91.32 ± 0.68	89.04 ± 1.92	96.78 ± 0.07	89.01 ± 0.83	97.46 ± 0.39	96.78 ± 0.69	98.60 ± 0.19

, our FDM-Net achieves SOTA results with 98.78% OA, 94.55% AA and 98.60% Kappa, surpassing the second-best GSCViT by 1.01% in OA. Compared algorithms suffer from dramatic accuracy degradation on minority crop classes with scarce training samples, whereas our frequency-domain feature mining framework achieves steady high recognition accuracy across all categories, demonstrating strong robustness against imbalanced data distribution. On minority classes, the advantage is pronounced: FDM-Net reaches 96.58% on Class 1 where MSDAN drops to 49.78%, and attains 80.00% on Class 9 where competing methods exhibit deviations exceeding 43%, confirming the robustness of the frequency-decoupled design under extreme sample scarcity.

The classification maps of various methods are shown in Figure 7, their classification maps exhibit noticeable misclassified regions within large farmland areas, along with blurred field edges and distorted outlines of tiny cropland parcels. These errors arise because compared methods focus primarily on local pixel relationships and struggle to capture both global context and fine boundary details simultaneously. In contrast, FDM-Net produces classification maps that are significantly closer to the ground truth. Benefiting from the decoupled modeling of low-frequency global contextual information and high-frequency boundary features, FDM-Net retains the complete geometric shape of scattered small farm plots and maintains high spatial consistency across homogeneous regions. These visual results confirm that FDM-Net effectively accommodates the fine-grained classification demands of complex agricultural landscapes.

4.4. Visual Radar Chart Analysis

As shown in Figure 8a, FDM-Net achieves the optimal OA across all five datasets, obtaining 97.58% (QHUP), 95.07% (QHUQ), 97.58% (QHUT), 94.79% (Houston), and 98.78% (IP). It outperforms the best method on each dataset by 0.54%, 0.57%, 0.76%, 0.28%, and 1.01%, respectively, demonstrating outstanding overall classification generality under diverse scene distributions. The AA radar chart in Figure 8b further validates the balanced class-level performance of FDM-Net. Our method achieves leading AA values on QHUP (92.35%) and QHUT (93.86%), along with competitive AA on QHUQ (88.57%), Houston (94.24%), and IP (94.55%). It surpasses Lite-HCNet by up to 2.57%, showing superior capability in handling hard and minority classes. Consistent performance gains are also observed in the Kappa metric in Figure 8c. FDM-Net achieves the highest Kappa scores on all datasets (96.39%, 93.47%, 97.25%, 94.39%, 98.60%), with consistent improvements over Lite-HCNet. Its fuller and more balanced radar coverage demonstrates stronger cross-dataset generalization. Collectively, the consistent OA, AA and Kappa superiority verifies that the collaborative design of FDE for frequency-aware decomposition and MLFA for multi-level spatial aggregation effectively enhances spectral–spatial feature discrimination and overall classification robustness.

4.5. Sensitivity Analysis

A sensitivity analysis evaluated the impact of multi-scale fusion weights ($w_0$, $w_1$, $w_2$ for fine to coarse scales, summing to 1) on classification accuracy, as reported in

Table 6. Sensitivity analysis of multi-scale fusion weights.

Row	${\mathit{w}}_0$	${\mathit{w}}_1$	${\mathit{w}}_2$	OA (%)
R1	0.70	0.20	0.10	91.42
R2	0.60	0.25	0.15	93.51
R3	0.50	0.30	0.20	94.12
R4	0.40	0.40	0.20	93.13
R5	0.33	0.33	0.34	84.23
R6	0.30	0.50	0.20	93.36
R7	0.20	0.30	0.50	93.68
R8	0.15	0.25	0.60	92.91

Bold value indicates the best result.

. Results show that fine-scale information dominates performance: the optimal configuration R3 ($w_0=0.50$, $w_1=0.30$, $w_2=0.20$) achieved the highest OA of 94.12%, confirming that a descending weight distribution ($w_0>w_1>w_2$) yields the most discriminative representation. Overemphasizing fine details R1 ($w_0=0.70$) reduced OA to 91.42% due to noise amplification, while moderate coarse-scale emphasis (R7, $w_0=0.20$, $w_1=0.30$, $w_2=0.50$) gave the second-best OA of 93.68%, but further increasing $w_2$ to 0.60 in R8 lowered it to 92.91%. The uniform allocation R5 ($w_0=0.33$, $w_1=0.33$, $w_2=0.34$) performed poorly (84.23%), about 9.9% below the optimum, indicating asymmetric contributions and feature dilution. Excluding R5, the other seven configurations showed OA within a narrow 91.42–94.12% range (2.70% spread), demonstrating robustness to weight variations across a broad operational range.

4.6. Ablation Study

4.6.1. Effectiveness of FDE and MLFA

The proposed FDM-Net contains two core modules: the Frequency Decomposition Enhancement (FDE) module and the Multi-Level Feature Aggregation (MLFA) module. To quantitatively verify the individual effectiveness of the two designs, we conduct ablation experiments by removing each module separately while keeping other network settings unchanged. Experimental results across five datasets consistently validate that both FDE and MLFA positively boost classification performance and model stability. Specifically, the FDE module addresses the frequency-specific bias problem in hybrid frameworks by explicitly decoupling input features into low-frequency global semantic information and high-frequency local detail features, thereby eliminating feature interference and enabling discriminative spectral–spatial representation learning. Meanwhile, the MLFA module tackles the insufficient exploitation of multi-level feature interactions by adaptively aggregating multi-level spatial details within the high-frequency branch, effectively preserving fine-grained structures that are critical for distinguishing spectrally similar and sample-scarce categories. Moreover, the two modules are mutually reinforcing: FDE supplies MLFA with spectrally purified high-frequency features via frequency decoupling, while MLFA preserves fine-grained spatial structures that complement the low-frequency global semantics, together yielding consistent gains over each module in isolation.

Taking the QHUP dataset as an example, as shown in

Table 7. Ablation study of the proposed FDM-Net on all datasets.

Dataset	MLFA	FDE	OA (%)	AA (%)	Kappa (%)
QHUP	✓	✓	97.58	92.35	96.39
	✓		96.49	91.29	95.20
		✓	96.52	91.40	95.41
QHUQ	✓	✓	95.07	88.57	93.47
	✓		94.11	87.63	92.17
		✓	94.03	87.58	92.54
QHUT	✓	✓	97.58	93.86	97.25
	✓		97.41	92.56	96.08
		✓	97.06	92.85	96.29
Houston	✓	✓	94.79	94.24	94.39
	✓		93.82	93.25	93.41
		✓	93.91	93.34	93.49
IP	✓	✓	98.78	94.55	98.60
	✓		97.86	93.74	97.71
		✓	97.95	93.88	97.83
✓ indicates the module is included; Bold values indicate the best results.

, removing MLFA reduces OA, AA, and Kappa to 96.52%, 91.40%, and 95.41% (drops of 1.06%, 0.95%, and 0.98%), while removing FDE yields 96.49%, 91.29%, and 95.20% (drops of 1.09%, 1.06%, and 1.19%). Similar trends are observed on QHUQ and QHUT, where both variants consistently underperform the full model in OA and Kappa, confirming the effectiveness of MLFA and FDE in improving discriminative feature learning. On Houston and Indian Pines, the full model also achieves the best OA, with clear margins over both ablated variants, highlighting their importance for complex and imbalanced scenes.

4.6.2. Ablation Study on the Gate Path in MLFA

The MLFA module adopts a dual-path design comprising a Gate Path and a Value Path. To verify the effectiveness of this gating mechanism, we construct a variant that removes the Gate Path entirely while retaining the Value Path and the FDE module.

Table 8. Ablation study of the Gate Path on all datasets.

Dataset	Gate Path	OA (%)	AA (%)	Kappa (%)
QHUP	✓	97.58	92.35	96.39
	×	96.68	82.16	95.05
QHUQ	✓	95.07	88.57	93.47
	×	95.06	88.86	93.45
QHUT	✓	97.58	93.86	97.25
	×	96.21	91.86	95.68
Houston	✓	94.79	94.24	94.39
	×	92.97	91.07	92.40
IP	✓	98.78	94.55	98.60
	×	93.64	83.02	92.73
✓ indicates the module is included; × indicates the module is not included. Bold values indicate the best results.

reports the comparison across all five datasets.

Removing the Gate Path leads to consistent performance degradation across all five datasets. On IP, OA drops sharply from 98.78% to 93.64% (−5.14%); on Houston and QHUT, the declines are 1.82% and 1.37%; on QHUP, OA falls by 0.90% with AA decreasing by 10.19%. Even on QHUQ (6 classes), the full model achieves slightly higher OA (95.07% vs. 95.06%). These results conclusively demonstrate that the Gate Path, despite its simple form, proves essential for adaptively modulating multi-scale spatial features.

Notably, its contribution is more pronounced on datasets with higher intra-class variability and more categories (e.g., IP with 16 classes, Houston with 15 classes), consistent with the expectation that gating-based feature selection becomes increasingly critical as feature space complexity grows.

4.6.3. Superiority of Mamba over Alternative Architectures

The low-frequency branch of FDM-Net employs a Mamba-based state space model for long-range dependency modeling. To justify this design choice, we replace the Mamba module with a Transformer Encoder of comparable parameter count while keeping all other components (FDE, MLFA with Gate Path) unchanged.

Table 9. Ablation study of the Mamba module on all datasets.

Dataset	Mamba	Transformer	OA (%)	AA (%)	Kappa (%)
QHUP	✓		97.58	92.35	96.39
		✓	96.17	78.49	94.28
QHUQ	✓		95.07	88.57	93.47
		✓	94.38	86.39	92.55
QHUT	✓		97.58	93.86	97.25
		✓	95.91	87.98	95.34
Houston	✓		94.79	94.24	94.39
		✓	93.91	93.34	93.49
IP	✓		98.78	94.55	98.60
		✓	96.24	94.36	95.71
✓ indicates the module is used. Bold values indicate the best results.

reports the comparison.

Across all five datasets, the Mamba-based branch consistently outperforms the Transformer-based alternative. On QHUT and IP, Mamba achieves OA improvements of 1.67% and 2.54%, respectively; on QHUP, the AA gap reaches 13.86%, demonstrating that Mamba’s state-space formulation is more effective than self-attention at capturing long-range spectral–spatial dependencies in hyperspectral data. This advantage stems from Mamba’s linear complexity and selective scan mechanism, which efficiently models global context without the quadratic overhead of Transformer self-attention, making it particularly suitable for the low-frequency branch where global semantic reasoning is required.

4.6.4. t-SNE Visualization

For qualitative analysis, t-SNE visualization is conducted on the Houston dataset (Figure 9) to compare the full FDM-Net, the FDE-only branch, and the MLFA-only branch. The FDE-only variant, which relies primarily on frequency-decomposed global context without multi-level spatial aggregation, exhibits noticeable inter-class overlap, particularly among spectrally similar categories. The MLFA-only variant improves local compactness through multi-level spatial feature aggregation but still suffers from scattered intra-class distributions due to the absence of explicit Frequency Decomposition. In contrast, the full FDM-Net produces the most compact intra-class clusters and the clearest inter-class separation, demonstrating that the FDE strategy and the MLFA module are complementary and jointly enhance feature discriminability.

Overall, both quantitative ablation results and qualitative t-SNE visualizations demonstrate that the Gate Path, Mamba branch, FDE, and MLFA modules are indispensable and mutually complementary. The cooperative integration of explicit Frequency Decomposition, gated multi-level spatial aggregation, and Mamba-based global context modeling enables FDM-Net to fully exploit spectral–spatial cues, thereby achieving superior and stable classification performance in complex hyperspectral scenarios.

4.7. Analysis of Model Complexity and Inference Efficiency

Experiments on the Houston dataset use an 11 × 11 input patch size, batch size 256, and PCA-reduced spectral dimension from 144 to 16. All models are evaluated under identical settings in terms of parameters, FLOPs, and inference time (

Table 10. Comparison of model complexity and inference efficiency on the Houston dataset.

Model Name	Params (MB)	FLOPs (M)	Inference Time (ms/Batch)
Lite-HCNet	0.01	0.320	17.466
LSSAN	0.15	5.990	15.873
MSDAN	12.75	442.135	43.611
SimPoolFormer	5.45	55.967	8.812
CacfNet	0.44	2.039	6.699
SpectralFormer	0.40	1.749	2.845
GSCViT	0.50	4.625	4.098
SSFTT	0.34	1.925	2.386
FDM-Net (our)	0.19	2.302	15.322

).

MSDAN exhibits the highest complexity (12.75 MB, 442.135 M FLOPs, 43.611 ms) due to its multi-scale convolutional branches. SimPoolFormer also incurs relatively high cost (5.45 MB, 55.967 M FLOPs) owing to its Transformer-based architecture. In contrast, Lite-HCNet, CacfNet, SpectralFormer, and SSFTT are extremely lightweight (≤0.44 MB, ≤2.04 M FLOPs), with SSFTT achieving the fastest inference (2.386 ms) thanks to its efficient tokenization and compact Transformer design. GSCViT maintains moderate complexity (0.50 MB, 4.625 M FLOPs) with competitive inference speed (4.098 ms).

Our FDM-Net achieves the best overall classification performance while maintaining low model complexity (0.19 MB, 2.302 M FLOPs), using only 1.49% of MSDAN and 3.49% of SimPoolFormer parameters. Although its inference time (15.322 ms) is higher than some extremely lightweight models due to multi-branch frequency-domain fusion, it remains 64.9% faster than MSDAN. Overall, FDM-Net strikes a favorable balance between state-of-the-art accuracy and acceptable computational cost by combining frequency-domain enhancement with multi-level spatial aggregation, making it suitable for resource-constrained hyperspectral applications.

5. Discussion

Several conclusions can be drawn regarding the role of the Frequency Decomposition Fusion Enhancement (FDE) strategy and the Multi-Level Feature Aggregation Module (MLFA). First, the classification results of these experiments on multiple public HSI benchmarks demonstrate that FDM-Net can effectively separate and process low-frequency global semantics and high-frequency spatial details through the proposed frequency-aware framework, leading to superior classification performance. Furthermore, these experiments reveal that conventional hybrid CNN–Mamba methods suffer from the frequency-specific feature preference mismatch. This can be verified by the fact that feeding homogeneous features into both branches results in significant feature interference and redundant representations, whereas FDM-Net explicitly routes frequency-decomposed components to their most suitable modeling branch, thereby resolving this fundamental limitation. Notably, FDE’s contribution varies with dataset characteristics: 0.97% and 0.92% on Houston and IP (spectrally driven) versus 1.09% on QHUP. This is because on spectrally dominated scenes, FDE mainly suppresses high-frequency noise, while on QHUP, where rich spatial structures coexist with spectral cues, both branches benefit more evenly, yielding the largest combined gain.

What is more, the MLFA module is introduced into the high-frequency branch to capture multi-level frequency interactions. Through depthwise and dilated convolutions followed by feature concatenation and nonlinear fusion, the MLFA module enables effective channel interaction and contextual modeling across multiple receptive field scales. This design addresses the limitation of CNNs that are inherently biased toward single-scale spatial interactions, allowing FDM-Net to exploit complex multi-level information components that would otherwise be underutilized. The contribution of MLFA also varies across datasets. The OA drop is largest on QHUQ (1.04%) and QHUT (0.52%), whose dense urban structures and fine-grained textures, respectively, benefit from spatial detail preservation. On Houston and IP, the drop is smaller (0.88% and 0.83%), likely because these datasets rely more on spectral cues than on fine spatial structures. The ablation studies further confirm that both the FDE strategy and the MLFA module contribute substantially to the overall performance, validating that the holistic frequency-aware design—rather than any single module in isolation—distinguishes FDM-Net from existing approaches. Nevertheless, FDM-Net exhibits limitations tied to its decomposition strategy. On QHUT Class 12 and Class 14, it trails GSCViT by 8.80% and 0.06%, and on Houston Class 13, it lags SSFTT by 22.79%. These cases suggest that Gaussian filtering may fragment discriminative features spanning multiple frequency bands, pointing toward learned, class-adaptive decomposition as a future direction.

Although the proposed Frequency Decomposition framework achieves significant improvements on the evaluated benchmarks, it is worth noting that the current Gaussian filtering-based decomposition introduces additional hyperparameters, such as the kernel size and the number of filtering levels, which may require task-specific tuning. Moreover, the multi-branch design increases model complexity, and the isotropic Gaussian kernel may not capture anisotropic frequency patterns in complex scenes. Furthermore, the GAP-based predictor in FDE computes channel-wise weights via global average pooling, which may become unstable for minority classes as the pooled statistics are biased toward dominant classes; class-balanced pooling could mitigate this issue. Furthermore, the multi-level Gaussian filtering is achieved through depthwise separable convolution, which can be directly computed in parallel on the GPU and does not introduce additional learnable parameters. Although increasing the decomposition levels will bring certain computational load and inference delay, the overall increase in cost is relatively limited. Finally, the actual range of the fixed-scale Gaussian kernel varies in different spatial resolution images, so its cross-resolution applicability still needs to be further verified. In the future, the filtering scale can be adaptively adjusted according to the ground sampling distance of the image to improve the model’s adaptability to different resolution data.

Future work could explore learnable, class-adaptive Frequency Decomposition to reduce feature fragmentation, lightweight filtering substitutes and more compact branch designs to lower model complexity, and GSD-aware decomposition for multi-resolution generalization. Additionally, while this work focuses on the integration of Mamba and CNNs under the frequency-aware paradigm, the proposed FDE strategy is potentially applicable to other hybrid architectures. The work in this paper provides certain reference values for subsequent research into frequency-aware feature learning and multi-level aggregation in hyperspectral image classification.

6. Conclusions

In this article, a novel Multi-Level Feature Aggregation Network based on Frequency Decomposition is proposed for hyperspectral image classification. Considering the homogeneous feature preferences across branches and insufficient multi-level information interaction modeling in existing HSI methods, the proposed FDM-Net uses a Frequency Decomposition Fusion Enhancement (FDE) strategy to decompose information into high and low frequencies and then sends this information to the corresponding high- and low-frequency-sensitive branches and a Multi-Level Feature Aggregation Module (MLFA) that effectively addresses the constraints of CNNs in capturing deep multi-level interactions. Extensive experiments conducted on five public HSI datasets demonstrate that FDM-Net achieves state-of-the-art performance, validating its effectiveness and superiority over existing counterparts.

This work advances HSI classification by establishing a frequency-aware feature learning paradigm that resolves branch-wise feature preference mismatches and captures high-order spatial interactions. The proposed components are adaptable to other remote sensing tasks such as semantic segmentation and object detection, with practical value in precision agriculture, mineral exploration, and environmental monitoring. Future work includes extending FDM-Net to multi-source data fusion, developing lightweight variants for real-time deployment, and exploring semi-supervised learning to mitigate label scarcity.