Enhanced Lightweight Image Super-Resolution via Residual Aggregation and Wavelet Loss

Abstract

Image super-resolution (SR), which aims to reconstruct a high-resolution image from a low-resolution input, has progressed from convolutional neural networks (CNNs) to transformer-based architectures. Despite this progress, lightweight transformer SR remains challenging: local or window-based operations provide limited long-range interaction, conventional query-key-value projections introduce parameter and computational redundancy, and pixel-domain loss alone provides insufficient frequency-domain constraints on fine structures. This study presents RAW, a lightweight SR network based on residual aggregation and wavelet loss. RAW uses local aggregation to preserve neighborhood textures, mesoscale grouped-residual attention to reduce projection redundancy while modeling regional dependencies, and non-local sparse aggregation to capture long-range information at a controlled cost. By integrating stationary-wavelet-transform loss with RGB-domain L1 loss, the model supervises structural and high-frequency information without adding an inference branch. Experiments on standard benchmarks demonstrate a competitive trade-off between reconstruction quality and computational complexity. For 4× SR, RAW reduces the numbers of parameters and MACs by 14.3% and 15.4%, respectively, relative to the baseline, while improving the PSNR and SSIM on Manga109 by 0.22 dB and 0.0015, respectively.

1. Introduction

Single-image super-resolution (SISR) is an important task in computer vision that involves reconstructing a visually sharp and detailed high-resolution image from a low-resolution input. Driven by rapid advances in deep learning, SISR techniques have transitioned from being based on conventional convolutional neural network frameworks to becoming grounded in transformer-based architectures. The SRCNN method, proposed in [1], is based on the convolutional neural network, and delivers impressive performance on SR tasks. It represents the first end-to-end deep learning-based approach that is specifically designed to address the challenges posed by SR. CNN-based SR techniques subsequently superseded classical interpolation methods [2,3]. Propelled by advances in transformer models [4], ViT-based super-resolution frameworks [5] have recently emerged, and have shown marked improvements in SR performance. Compared with earlier CNN-based approaches, transformer-based models excel at capturing long-range dependencies to improve the quality of the reconstructed images. Researchers have lately proposed hybrid SR networks [6] that fuse the components of the transformer and CNN to exploit their respective strengths. Despite the substantial advances in deep learning-based SISR, most research in the area has targeted large-scale architectures, while the development of lightweight models (with under 1 M parameters) remains challenging. Lightweight SISR requires a careful balance among reconstruction quality, parameter efficiency, and computational cost, making it impractical to rely solely on increasing network depth or feature dimensions. The challenges also differ across spatial ranges. Local convolutions efficiently recover edges and neighborhood textures but have limited receptive fields; window-based attention captures mesoscale relationships but is restricted by window boundaries; and dense global attention introduces substantial computational overhead. In particular, the self-attention mechanism used in transformer-based SR may involve considerable computational redundancy [7]. To improve its efficiency, Ref. [8] introduced a grouped multi-scale self-attention module that divides input features into groups and applies attention windows of different sizes to model multi-scale dependencies while controlling computational cost. Similarly, Ref. [9] proposed a linear residual grouping strategy for the conventional query, key, and value projections, thereby reducing projection redundancy, parameter count, and computational overhead. Moreover, RGB-domain L1 loss alone provides limited supervision for frequency-domain structures.

Currently available lightweight models are limited in terms of the diversity of their design, and use a single attention mechanism, single-scale handling, and uniform network structures. To overcome these limitations, Ref. [10] introduced a transformer-based deep global processing scheme that substitutes convolutional locality to endow the model with convolution-like spatial biases such that it can efficiently capture global representations. Reference [11] proposed a multi-scale attention network (MAN) for SISR that fuses the CNN and attention to deliver impressive SR performance, all the while achieving an optimal trade-off between the accuracy and footprint of the model at different levels of complexity. Moreover, to capture intricate high-frequency details, researchers have investigated techniques of frequency-domain processing for SR. While wavelet transforms have been applied to SR, their integration into transformer-based architectures is still in its infancy. Whereas prevalent research relies on the L1 loss, Ref. [12] pioneered the incorporation of wavelet loss into transformer-based SR models by introducing a wavelet sub-band loss term that overcomes the limitations of RGB pixel loss in capturing high-frequency details to enhance the fidelity of the reconstruction.

Motivated by recent advances in hierarchical feature aggregation, grouped-residual attention, and wavelet-domain supervision [6,9,12], we propose RAW, a lightweight image super-resolution network that combines residual aggregation with wavelet-domain loss. RAW is designed to balance reconstruction quality, parameter efficiency, and computational cost by coordinating feature interactions across different spatial ranges and introducing complementary frequency-domain supervision. Against this background, each component of RAW is designed to address a distinct requirement of lightweight SR. Specifically, LAB extracts local texture features through efficient convolution; MRGAB employs grouped-residual attention to model mesoscale interactions while reducing projection redundancy; NLSAB provides sparse long-range information aggregation at a controlled computational cost; and the SWT loss complements spatial-domain L1 supervision by imposing subband-level constraints. Together, these components address the local, mesoscale, non-local, and frequency-domain requirements of lightweight SR.

The main contributions of this work are summarized as follows:

• We develop a lightweight SISR architecture that organizes feature aggregation across local, mesoscale, and non-local spatial ranges. LAB preserves neighborhood textures, MRGAB integrates grouped-residual attention for efficient regional interaction, and NLSAB captures long-range dependencies through sparse aggregation.
• We integrate grouped residual linear projections into the mesoscale RGSA stage to reduce redundancy in conventional query, key, and value projections. This design coordinates efficient mesoscale interaction with the local features extracted by LAB and the non-local information aggregated by NLSAB.
• We introduce a composite training objective that combines RGB-domain L1 loss with SWT-domain supervision. The SWT loss explicitly constrains low-frequency structures and directional high-frequency details without introducing an additional inference branch.
• Experiments on five standard benchmark datasets demonstrate that RAW achieves a competitive trade-off between reconstruction quality and model complexity. For $4\times$ SR, the complete model reduces the parameter count and MACs by 14.3% and 15.4%, respectively, relative to the baseline, while improving the PSNR and SSIM on Manga109 by 0.22 dB and 0.0015, respectively.

2. Related Work

We now review CNN- and transformer-based methods and attention mechanisms that are pertinent to our proposed method.

2.1. CNN- and Transformer-Based SR Methods

SISR has evolved from being based on techniques of classical interpolation to deep learning-based paradigms. The SRCNN, introduced by Dong et al. [1], was the first instance of CNN-based end-to-end mapping via a three-layer convolutional network. Kim et al. [13] subsequently proposed the VDSR by leveraging residual learning to extend the depth of the network to 20 layers. The EDSR [14] achieved significant benchmark improvements by eliminating batch normalization layers and adopting channel expansion. The RCAN [15] developed by Zhang et al. further integrated channel attention to improve the PSNR on standard benchmarks. The advent of the transformer model provides new opportunities and challenges for SISR. SwinIR [16] pioneered window-based attention in image restoration. Its hierarchical design preserves linear complexity, and yielded a 0.39 dB increase in the PSNR over the RCAN on the 4× task in Urban100. The pure transformer-based IPT [17] models global attention via pre-training, but its substantial requirements pertaining to the data and computation as well as its complexity hinder its empirical deployment. Consequently, hybrid designs have garnered greater interest. The ESRT [18], developed by Lu et al., introduces a lightweight transformer–CNN interaction module that reduces the number of required computations to a ninth of the cost of the VDSR. In addition to CNN- and Transformer-based approaches, autoencoder architectures have also been investigated for image SR. Zhou et al. [19] introduced dense convolutional autoencoder blocks that extract multi-resolution features through paired encoding–decoding layers and facilitate feature reuse through skip and dense connections.

We investigate a hybrid architecture by using a module for global residual aggregation to improve the capability of the model to distinguish between multi-level features. We also integrate self-attention and sparse attention to bolster the capabilities of the global module for feature extraction.

2.2. Attention Mechanism

Dai et al. [20] pioneered self-attention in the SAN. This second-order attention module yielded an improvement of 0.20 dB in the PSNR on Set5 under 4× upscaling. PANet [21] introduces a pyramid attention structure that leverages interactions between features at multiple scales to reconstruct complex textures. The HAN [22] combines channel and spatial attention to boost the SSIM on Urban100’s 4× SR challenge to 0.8131.

A number of attention-based enhancements have been incorporated into the SR task. However, approaches based on global attention suffer from two critical drawbacks: inherent redundancy and an excessively high computational cost. For instance, SwinIR reduces its number of parameters to 11.8 M by using windowed attention, but still takes about 1.1 s to process images of the same resolution, whereas the CNN-based RCAN takes only 0.2 s. Moreover, even when SwinIR is reduced to six heads and C = 60 in lightweight trials, it still incurs 87.2 G MACs (3×) or 49.6 G MACs (4×), which reflects redundancy in contrast with IMDN’s costs of 71.5 G and 40.9 G, respectively [23].

GRFormer reduces query-key-value projection redundancy through grouped-residual self-attention [9], whereas OmniSR aggregates local, mesoscale, and global information to enlarge the effective receptive field [24]. Building on these ideas, RAW places grouped-residual projection specifically within the mesoscale RGSA stage and coordinates it with local convolution and non-local sparse aggregation. In addition, RAW incorporates SWT-domain supervision only during training to provide complementary frequency-domain constraints.

3. Proposed Method

3.1. Framework

Figure 1 shows the overall pipeline of RAW together with an expanded residual aggregation block (RAB). The upper part consists of shallow-feature extraction, sequential RABs for deep-feature extraction, and an image-reconstruction module. The lower part expands one RAB to illustrate how features successively pass through LAB, MRGAB, and NLSAB, thereby extending feature aggregation from local neighborhoods to mesoscale regions and non-local positions. RGSA serves as an internal attention submodule of MRGAB rather than an independent stage in the overall pipeline. RAW adopts a sequential backbone [25] and adapts the omni-scale aggregation principle [24] through grouped-residual projection and non-local sparse interaction. During training, the reconstruction objective is further complemented by SWT-domain supervision to strengthen the recovery of structural and high-frequency information.

3.2. Residual Aggregation Block (RAB)

Window-based self-attention that is implemented through hierarchical stacking is the predominant design in current research. However, there are notable deficiencies in the efficiency of its long-range interactions, especially in shallow layers. We introduce the residual aggregation block (RAB), which is an efficient global interaction module that enables the progressive aggregation of features of the receptive field at a minimal computational cost. The RAB comprises three core components: a local aggregation block (LAB), a mesoscale residual grouping aggregation block (MRGAB), and a non-local sparse aggregation block (NLSAB).

The LAB is a lightweight, highly efficient convolutional module that integrates pointwise and depthwise convolutions, GELU activation, and SE-based channel attention. The SE module adaptively reweighs channel-wise features to improve the representational power of the model. Designed to reduce the computational cost via depth-separable convolutions, the LAB leverages the SE to improve the efficiency of the CNN while aggregating the local context to enhance its capacity for training. Given an input image $LR\in R^{HW{C}_{in}}$ ($C_{in}$ represents the input channel), the LAB extracts shallow features and projects inputs from the spatial domain into a high-dimensional feature space:

$$X_{SF}=H_{SF}\left(I_{LR}\right)$$

(1)

where $X_{SF}$ denotes the extracted shallow features and $H_{SF}$ refers to the LAB.

The MRGAB is designed for mesoscale feature aggregation and consists of RGSA and a mesoscale channel-attention mechanism. As illustrated by the expanded RAB in Figure 1, RGSA is implemented as an internal attention submodule within MRGAB, rather than as a separate stage alongside LAB and NLSAB. Following the design of GRFormer [9], RGSA replaces the conventional query, key, and value linear projections with grouped residual linear (GRL) projections. Group-wise processing combined with residual connections reduces projection redundancy, parameter count, and computational cost while preserving effective feature interaction. In RAW, the GRL-based RGSA is integrated into the mesoscale aggregation stage, where it works together with the local feature extraction of LAB and the non-local sparse aggregation of NLSAB. Specifically, the GRL splits the input features along the channel axis into two independent subgroups, each of which is handled by its own linear residual transformation branch. Given an input $x\in R^{B\times N\times D}$ (with B as the batch size, length of sequence N, and D feature dimensions), the GRL initially partitions it into $x_1,x_2\in R^{B\times N\times {\displaystyle \frac{D}{2}}}$. Then, each subgroup applies its own linear transformation to generate local features, which are combined with the original subgroup via residual connections. Finally, the outputs of the two subgroups are concatenated along the channel axis to yield the full query (Q), key (K), and value (V). This procedure can be formulated as follows:

$$\widehat{q_i}=x_i+W_q^{\left(i\right)}\left(x_i\right)$$

(2)

$$\widehat{k_i}=x_i+W_k^{\left(i\right)}\left(x_i\right)$$

(3)

$$\widehat{v_i}=x_i+W_v^{\left(i\right)}\left(x_i\right)$$

(4)

where $x_i$ represents the i-th($i\in \left\{1,2\right\}$) partition of the input tensor in $R^{B\times N\times {\displaystyle \frac{D}{2}}}$, and $W_q^{\left(i\right)}$, $W_k^{\left(i\right)}$, and $W_v^{\left(i\right)}$ are the linear projection matrices for Q, K, and V, respectively, of the partition, each in $R^{B\times N\times {\displaystyle \frac{D}{2}}}$. The terms $\widehat{q_i}$, $\widehat{k_i}$, and $\widehat{v_i}$ denote the Q, K, and V vectors, respectively, post-residual fusion in the i-th subgroup. In summary, the MRGAB processes the feature maps as follows: The RGSA first partitions the input feature $X\in R^{B\times C\times H\times W}$ into non-overlapping $P\times P$ blocks, and maps the spatial dimension blocks $(H,W)$ into $({\displaystyle \frac{H}{P}}\times P,{\displaystyle \frac{W}{P}}\times P)$. Then, these patches are stacked back into the spatial dimensions to generate the updated feature map $X^{\prime }\in R^{B\times {\displaystyle \frac{HW}{P^2}}\times P^2\times C}$. By decomposing the global spatial context into local windows, this approach facilitates interactions between features at the mesoscale. Finally, the channel attention module inside each window optimizes inter-channel dependencies to strengthen feature integration across channels.

The NLSAB is centered on a non-local sparse attention mechanism for global feature aggregation and the modeling of long-range dependencies, as illustrated in Figure 1. It consists of locality-sensitive hashing (LSH), followed by an attention computation stage. LSH partitions the feature $x\in R^{B\times C\times H\times W}$ into buckets of similar content, and restricts attention to intra- and inter-bucket interactions. Attention is then computed by ranking the buckets via their hash codes, and by calculating weights within and across neighboring buckets to capture both local and global dependencies.

Specifically, for the LSH operation, we first compute the input similarity to derive an intermediate feature encoding z, which acts both as the query vector in the attention mechanism and the foundation for the hash codes. We then apply a random projection to map z onto the unit hypersphere and normalize it. This procedure can be formulated as follows:

$$\widehat{Z}={\displaystyle \frac{z}{{\left|\left|z\right|\right|}_2}}$$

(5)

where $\widehat{Z}\in R^{B\times L\times C}(L=H\times W)$ represents the normalized vector.

Subsequently, the normalized vector is rotated via a random rotation matrix $A\in R^{c\times k}$. This is represented as

$$Z^{\prime }=A\left(\widehat{Z}\right)$$

(6)

Finally, the rotated vector $Z^{\prime }$ is allocated to one of k hash buckets. At each position $i\in \left\{1\dots L\right\}$, the index of the maximum entry in $z_i^{\prime }$ is selected as the hash code to ensure that similar (directionally proximate) vectors are more likely to map to the same bucket post-rotation. This can be formulated as follows:

$$h\left(z\right)=argmax\left(z^{\prime }\right)$$

(7)

where $h\left(z\right)$ represents the hash code. This mechanism makes similar vectors more likely to map to the same bucket post-projection, and allows the feature vectors to be ordered by their hash codes.

Once bucketing is complete, we calculate the attention weights between each query vector and all feature vectors within the same bucket. This attention mechanism captures local dependencies within each bucket by applying attention scores to weigh and aggregate the corresponding feature values.

3.3. Loss Function

Many lightweight SR models rely solely on a single loss function (e.g., L1 loss) during training. However, when restoring high-frequency details, its effect is often limited, and this strategy is prone to generating artifacts. To mitigate this issue, we adopt a composite loss that integrates loss from the wavelet domain with the traditional L1 loss to improve the capability of the model to discriminate between genuine high-frequency details and spurious artifacts. Despite some early applications of wavelet domain loss, its integration into transformer-based SR models for performance enhancement remains rare.

The stationary wavelet transform (SWT) decomposes an image across scales into a low-frequency approximation sub-band (LL) and multiple sub-bands of high-frequency detail (LH, HL, HH). Specifically, the LH sub-band captures horizontal details, the HL sub-band encodes vertical details, and the HH sub-band represents diagonal directional features. Given the vital role of the resolution in SR, the SWT outperforms the conventional discrete wavelet transform (DWT). Downsampling by using the traditional DWT in SR tasks often leads to the loss of high-frequency details, and is sensitive to image shifts that yield artifacts and a loss of the fidelity of detail. By preserving redundant frequency-related information, and eliminating downsampling and sensitivity to shifting, the SWT can restore the details of the image, particularly its high-frequency edges and textures.Benefiting from the absence of coefficient downsampling, SWT maintains the spatial resolution of each subband and yields translation invariance. This property eliminates spatial misalignment between the super-resolved result and the ground-truth high-resolution image, enabling pixel-wise comparison of wavelet coefficients. Subband supervision imposes explicit constraints on low-frequency structures and directional high-frequency components, serving as complementary guidance for the RGB-domain loss. In this work, we adopt a single-level 2-D SWT with the Symlet-19 (sym19) wavelet, applied only on the luminance channel using periodic boundary extension. This configuration is fixed in our implementation for reproducibility.

Figure 2 illustrates the computation of the SWT-domain loss during training. Given an LR input x and its corresponding HR target y, the proposed network first generates an SR image $\widehat{y}=G\left(x\right)$. The luminance components of the SR image and the HR target are then extracted and transformed using the same single-level two-dimensional SWT. The resulting coefficient maps are decomposed into four subbands, namely LL, LH, HL, and HH. The SWT-domain loss is calculated by comparing the corresponding subbands of the SR output and the HR target using the weighted L1 distance:

$$L_{\mathrm{SWT}}={\displaystyle \frac{1}{B}}{\displaystyle \sum _{i=1}^B}\sum _{j\in \{\mathrm{LL},\mathrm{LH},\mathrm{HL},\mathrm{HH}\}}{\lambda }_j{∥{\mathcal{S}}_j\left(Y\left({\widehat{y}}_i\right)\right)-{\mathcal{S}}_j\left(Y\left(y_i\right)\right)∥}_1$$

(8)

where B denotes the mini-batch size, ${\widehat{y}}_i=G\left(x_i\right)$ is the SR output for the i-th LR input, and $y_i$ is the corresponding HR target. The operator $Y(·)$ extracts the luminance channel, and ${\mathcal{S}}_j(·)$ denotes the SWT coefficient map of the j-th subband. Thus, $L_{\mathrm{SWT}}$ directly measures the differences between the corresponding wavelet coefficients of the SR output and the HR target. The subband weights are fixed as ${\lambda }_{\mathrm{LL}}=0.05$, ${\lambda }_{\mathrm{LH}}={\lambda }_{\mathrm{HL}}=0.025$, and ${\lambda }_{\mathrm{HH}}=0.02$. The LL subband receives the largest weight because it mainly represents low-frequency structural information, whereas the LH, HL, and HH subbands provide directional high-frequency information related to edges and fine textures. These weights are fixed throughout training and are not learned adaptively.

The total training loss is defined as

$$L_{\mathrm{total}}=L_{\mathrm{RGB}}+L_{\mathrm{SWT}}$$

(9)

where $L_{\mathrm{RGB}}$ is the RGB-domain L1 reconstruction loss between the SR output $\widehat{y}$ and the HR target y. During each training iteration, both $\widehat{y}$ and y are transformed into the luminance domain and processed by the same SWT operator to compute $L_{\mathrm{SWT}}$. The two loss terms are then summed to update the network parameters through backpropagation. The SWT operation is used only for training supervision and does not introduce an additional branch or computational operation during inference.

Overall, the contribution of RAW does not lie in proposing the GRL formulation itself, but in coordinating this existing projection strategy with LAB, NLSAB, and training-only SWT supervision to address local, mesoscale, non-local, and frequency-domain modeling requirements in lightweight SR.

4. Experimental Results and Analyses

4.1. Experimental Configuration

The experiments and code were executed on a Linux server with Ubuntu 22.04, featuring an NVIDIA RTX 4090 GPU with 24 GB of memory. We trained our model on the DIV2K dataset [26], which contained 800 training and 100 validation images. We tested it on five standard SR benchmarks: Set5 [27], Set14 [28], B100 [29], Urban [30], and Manga109 [31]. Its performance was quantified based on the PSNR and SSIM, which were measured on the luminance channel (Y) of the YCbCr color space.

We applied data augmentation via random horizontal flips and rotations during training. LR inputs were obtained through the bicubic downsampling of the HR images [32]. We trained the model by using Adam, with a batch size of 64 and over 800 K iterations. The initial learning rate was set to ${10}^{-4}$, and was reduced by 50% after every 200 K iterations. Each batch input consisted of randomly cropped 64 × 64 LR patches.

4.2. Comparison with State-of-the-Art Methods

We benchmarked our method against 13 state-of-the-art SR methods for $2\times$, $3\times$, and $4\times$ upscaling tasks: EDSR-baseline [14], LatticeNet [33], ShuffleMixer [34], ESRT [18], MFCC [35], AFAN [36], FDSCSR [37], SPAN [38], PCRN [39], EFRDN [40], MWDIN [41], RTFN [42], and DCAE-Multi [19].

Table 1. Quantitative evaluation of state-of-the-art SR algorithms: average PSNR/SSIM for scale factors $2\times$, $3\times$, and $4\times$. The best performance is shown in red and the second-best performance in blue (“-” indicates that the corresponding result is unavailable).

Scale	Method	Params (K)	MACs (G)	Set5	Set14	B100	Urban100	Manga109
				PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM	PSNR/SSIM
$2\times$	EDSR-baseline	1370	316.30	37.99/0.9604	33.57/0.9175	32.16/0.8994	31.98/0.9272	38.54/0.9769
	LatticeNet	756	169.50	38.15/0.9610	33.78/0.9193	32.25/0.9005	32.43/0.9302	-/-
	ShuffleMixer	394	45.05	38.01/0.9606	33.63/0.9180	32.17/0.8995	31.89/0.9257	39.83/0.9774
	MFCC	1861	364.50	38.16/0.9611	33.85/0.9195	32.28/0.9010	32.65/0.9331	39.11/0.9780
	AFAN	1208	289.50	38.06/0.9608	33.74/0.9198	32.20/0.9001	32.38/0.9305	38.79/0.9773
	FDSCSR	823	215.80	38.12/0.9609	33.69/0.9191	32.24/0.9004	32.50/0.9315	38.89/0.9775
	SPAN	481	-	38.08/0.9608	33.71/0.9183	32.22/0.9002	32.24/0.9294	38.94/0.9777
	PCRN	368	-	38.05/0.9611	33.62/0.9184	32.23/0.9000	32.23/0.9286	39.05/0.9779
	EFRDN	768	111.60	38.03/0.9609	33.65/0.9185	32.16/0.8997	32.34/0.9298	38.86/0.9776
	MWDIN	536	112.80	38.16/0.9614	33.97/0.9206	32.33/0.9021	32.58/0.9313	39.31/0.9785
	DCAE-Multi	-	-	37.74/0.9594	33.29/0.9144	32.05/0.8977	31.44/0.9207	-/-
	Ours	659	145.17	38.18/0.9619	33.88/0.9220	32.38/0.9024	32.95/0.9360	39.41/0.9786
$3\times$	EDSR-baseline	1555	160.10	34.37/0.9270	30.28/0.8417	29.09/0.8052	28.15/0.8527	33.45/0.9439
	LatticeNet	765	76.30	34.53/0.9281	30.39/0.8424	29.15/0.8059	28.33/0.8538	-/-
	ESRT	770	-	34.42/0.9268	30.43/0.8433	29.15/0.8063	28.46/0.8574	33.95/0.9455
	ShuffleMixer	415	21.50	34.40/0.9272	30.37/0.8423	29.12/0.8051	28.08/0.8498	33.69/0.9448
	MFCC	2230	374.10	34.67/0.9294	30.51/0.8456	29.22/0.8080	28.64/0.8616	34.15/0.9478
	AFAN	1208	143.10	34.46/0.9271	30.38/0.8436	29.11/0.8064	28.31/0.8556	33.61/0.9451
	FDSCSR	830	96.40	34.50/0.9281	30.43/0.8442	29.15/0.8068	28.40/0.8576	33.78/0.9460
	EFRDN	768	49.50	34.44/0.9275	30.38/0.8414	29.10/0.8059	28.29/0.8542	33.73/0.9453
	MWDIN	545	50.90	34.58/0.9290	30.48/0.8450	29.21/0.8093	28.43/0.8567	34.14/0.9471
	DCAE-Multi	-	-	34.12/0.9251	30.02/0.8353	29.00/0.8018	27.63/0.8394	-/-
	Ours	668	66.22	34.46/0.9304	30.25/0.8484	29.21/0.8112	28.89/0.8670	34.44/0.9501
$4\times$	EDSR-baseline	1518	114.20	32.09/0.8938	28.58/0.7813	27.57/0.7357	26.04/0.7849	30.35/0.9067
	LatticeNet	777	43.60	32.30/0.8962	28.68/0.7830	27.62/0.7367	26.25/0.7873	-/-
	ESRT	751	-	32.19/0.8947	28.69/0.7833	27.69/0.7379	26.39/0.7962	30.75/0.9100
	ShuffleMixer	411	14.00	32.21/0.8953	28.66/0.7827	27.61/0.7366	26.08/0.7835	30.65/0.9093
	MFCC	2157	395.20	32.42/0.8973	28.73/0.7849	27.67/0.7399	26.48/0.7977	30.98/0.9131
	AFAN	1226	90.10	32.30/0.8951	28.66/0.7838	27.61/0.7383	26.27/0.7913	30.63/0.9109
	FDSCSR	839	54.80	32.36/0.8970	28.67/0.7840	27.63/0.7384	26.33/0.7935	30.69/0.9113
	SPAN	498	-	32.20/0.8953	28.66/0.7834	27.62/0.7374	26.18/0.7879	30.66/0.9103
	PCRN	389	-	32.28/0.8964	28.68/0.7832	27.64/0.7369	26.21/0.7883	30.68/0.9105
	EFRDN	767	27.90	32.33/0.8964	28.67/0.7833	27.63/0.7384	26.37/0.7939	30.76/0.9113
	MWDIN	557	29.40	32.42/0.8987	28.77/0.7857	27.70/0.7415	26.38/0.7920	31.06/0.9134
	RTFN	-	-	32.26/0.8953	28.63/0.7818	27.61/0.7364	26.27/0.7887	30.55/0.9075
	DCAE-Multi	-	-	31.79/0.8895	28.31/0.7741	27.42/0.7291	25.66/0.7695	-/-
	Ours	680	38.32	32.41/0.8996	28.55/0.7887	27.80/0.7443	26.64/0.8033	31.32/0.9187

compares the performance and computational complexity of lightweight SR methods across the five benchmark datasets. The results showed that the RAW substantially outperformed all other methods for $2\times$, $3\times$, and $4\times$ upscaling, and achieved PSNR and SSIM scores that were on par with or better than those of the best current models on most benchmarks. Notably, on Manga109, which is rich in structured anime content, the RAW attains the best PSNR and SSIM at every scale. This underscores its suitability for applications that demand accurate, high-frequency detail and edge restoration. Furthermore, the RAW delivered these gains in performance with significantly fewer parameters compared to most competing methods, achieving a competitive trade-off between computational cost and reconstruction fidelity.

We visually compared five representative lightweight SR methods, namely EDSR, LatticeNet, ShuffleMixer, FDSCSR, and SPAN, under the $4\times$ super-resolution setting. The $4\times$ setting was selected because its more severe information loss makes the differences among the methods in edge recovery, texture reconstruction, and structural preservation more apparent. Figure 3, Figure 4 and Figure 5 present the reconstructed results of these methods on three representative test images, namely Set14-barbara, Set14-ppt3, and Urban100-img034. These visual comparisons provide representative qualitative evidence of the reconstruction performance of the evaluated methods.

The EDSR, LatticeNet, ShuffleMixer, FDSCSR, and SPAN all yielded prominent textural deformations and color biases on the Set14-barbara image. Especially acute was the loss of structural detail in the region of the bookshelf. By comparison, the RAW achieved superior color reproduction, with a PSNR of 24.86. The EDSR, LatticeNet, ShuffleMixer, FDSCSR, and SPAN generated letter reconstructions with blurred edges on the ppt3 text image, while the RAW recovered crisp and sharp character outlines. The RAW outperformed all other methods on the Urban-img034 sample in terms of reconstructing window-frame geometry, with an SSIM of 0.6105 (1.94% higher on average than competing models). This demonstrated its superior capability in retaining fine details.

4.3. Ablation Study

We conducted ablation experiments to investigate the effects of GRL projections, the NLSAB, and the SWT-domain loss on reconstruction performance and model efficiency.

Table 2. Model configurations for the ablation study of the proposed network. The four RAW variants are progressively constructed under a fixed component-addition order, enabling conditional comparisons between adjacent configurations.

Model	Baseline	GRL	NLSAB	SWT	Params/MACs
1	✓				792 K/45.29 G
2	✓	✓			732 K/41.67 G
3	✓	✓		✓	732 K/41.67 G
4	✓	✓	✓	✓	680 K/38.32 G

and

Table 3. Performance results of the ablation study on the proposed network. PSNR/SSIM values are reported for four progressively constructed RAW variants under a fixed component-addition order.

Model	Set5	Set14	B100	Urban100	Manga109
1	32.34/0.8992	28.56/0.7884	27.77/0.7433	26.57/0.8017	31.10/0.9172
2	32.39/0.8987	28.50/0.7875	27.75/0.7428	26.52/0.8007	31.15/0.9169
3	32.40/0.8991	28.51/0.7878	27.77/0.7434	26.60/0.8023	31.25/0.9175
4	32.41/0.8996	28.55/0.7887	27.80/0.7443	26.64/0.8033	31.32/0.9187

report four progressively enhanced configurations under the $4\times$ upscaling setting. Model 1 (baseline) uses only the core network. Model 2 augments the baseline with GRL projections. Model 3 builds upon Model 2 by incorporating the SWT-domain loss into the composite training objective, whereas Model 4 further introduces NLSAB to form the complete RAW architecture. All experiments follow the same progressive order of component addition. Therefore, the difference between two adjacent models measures the conditional incremental effect of the newly added component under this specific sequence, rather than its independent effect in a complete factorial design.

The experimental results reveal the distinct roles of the components within the fixed progressive ablation sequence. From Model 1 to Model 2, introducing GRL projections reduces the parameter count from 792 K to 732 K and the MACs from 45.29 G to 41.67 G, corresponding to reductions of 7.6% and 8.0%, respectively. Along with this efficiency improvement, slight decreases in PSNR and SSIM are observed on several datasets, whereas the PSNR on Manga109 increases by 0.05 dB. This result indicates that GRL primarily serves as an efficiency-oriented component designed to reduce computational overhead, rather than consistently improve reconstruction performance across all datasets. The minor precision trade-offs are acceptable for lightweight deployment. From Model 2 to Model 3, the SWT-domain loss is applied only during training and introduces no additional parameters or computational cost during inference. It improves the PSNR by 0.01 dB, 0.01 dB, 0.02 dB, 0.08 dB, and 0.10 dB on Set5, Set14, B100, Urban100, and Manga109, respectively, demonstrating that the frequency-domain constraint complements conventional RGB-domain supervision for high-frequency texture restoration. From Model 3 to Model 4, incorporating the NLSAB further reduces the parameter count to 680 K and the MACs to 38.32 G. At the same time, consistent improvements in PSNR are obtained on all five benchmark datasets, reaching 26.64 dB on Urban100 and 31.32 dB on Manga109.

All performance and complexity variations described above represent conditional incremental changes between adjacent model variants under the specified additive order, rather than standalone independent effects evaluated through a full-factorial experimental design. These progressive ablation results demonstrate that the complete combination of components in Model 4 achieves a favorable trade-off between computational efficiency and reconstruction quality.

5. Conclusions

In this study, we presented RAW, a lightweight image super-resolution method that combines residual aggregation with wavelet-domain supervision. The network organizes feature interaction across three spatial ranges: LAB extracts local textures, MRGAB introduces grouped-residual attention for mesoscale aggregation, and NLSAB captures non-local dependencies through sparse interaction. Within MRGAB, GRL projections reduce redundancy in the query, key, and value projections, thereby lowering the parameter count and computational cost, although they may also lead to small dataset-dependent fluctuations in PSNR and SSIM. During training, the RGB-domain L1 loss is combined with a single-level Symlet-19 SWT loss to constrain low-frequency structures and directional high-frequency details without introducing an additional inference branch. The complete configuration therefore reflects the combined efficiency–fidelity trade-off of GRL, SWT supervision, and NLSAB, rather than a uniform accuracy gain from every individual component. For $4\times$ upscaling, RAW reduces the parameter count and MACs by 14.3% and 15.4%, respectively, relative to the baseline. It also improves the PSNR and SSIM on Manga109 by 0.22 dB and 0.0015, respectively. Across five standard benchmark datasets, RAW achieves competitive reconstruction performance with a compact computational footprint. These results demonstrate that RAW can effectively integrate local, mesoscale, non-local, and frequency-domain information within a lightweight architecture. In particular, its favorable balance between reconstruction quality and computational efficiency highlights its practical potential for resource-constrained image restoration applications.

However, the current work has certain limitations. The proposed method is evaluated exclusively under the bicubic downsampling degradation model, and its performance under real-world complex degradations, such as noise, blur, and compression artifacts, remains to be explored. In future work, we plan to extend RAW to handle more realistic degradation scenarios and further optimize its inference efficiency for practical deployment on resource-constrained devices. In addition, we will investigate the effects of different wavelet bases, including Haar, Daubechies, and other wavelet families, through systematic ablation studies. This may provide a deeper understanding of the sensitivity of SWT-domain supervision to wavelet selection and the potential need to adapt the subband weighting scheme to different wavelet configurations.