Joint Deblurring and Destriping for Infrared Remote Sensing Images with Edge Preservation and Ringing Suppression

Highlights

What are the main findings?

• A unified three-stage variational framework is proposed for joint destriping and deblurring of infrared remote sensing images, integrating structure-tensor-based adaptive edge preservation, stripe-oriented fidelity constraints, and a new WCOB ringing-suppression model.
• The method achieves superior kernel estimation accuracy, better detail preservation, and stronger robustness compared with state-of-the-art destriping and deblurring techniques, consistently improving SSIM, PSNR, and NIQE across both simulated and real satellite datasets.

What is the implication of the main finding?

• By effectively removing stripe noise before kernel estimation and suppressing ringing artifacts during non-blind restoration, the proposed framework significantly enhances the clarity and reliability of infrared remote sensing imagery, benefiting downstream tasks such as target detection and environmental monitoring.
• The strong generalization capability demonstrated on Jilin-1 and SDGSAT-1 real data suggests that the proposed method has high practical applicability for operational remote-sensing imaging systems, providing a foundation for future integration with lightweight or deep-learning-based onboard processing.

Abstract

Infrared remote sensing images are often degraded by blur and stripe noise caused by satellite attitude variations, optical distortions, and electronic interference, which significantly compromise image quality and target detection performance. Existing joint deblurring and destriping methods tend to over-smooth image edges and textures, failing to effectively preserve high-frequency details and sometimes misclassifying ringing artifacts as stripes. This paper proposes a variational framework for simultaneous deblurring and destriping of infrared remote sensing images. By leveraging an adaptive structure tensor model, the method exploits the sparsity and directionality of stripe noise, thereby enhancing edge and detail preservation. During blur kernel estimation, a fidelity term orthogonal to the stripe direction is introduced to suppress noise and residual stripes. In the image restoration stage, a WCOB (Non-blind restoration based on Wiener-Cosine composite filtering) model is proposed to effectively mitigate ringing artifacts and visual distortions. The overall optimization problem is efficiently solved using the alternating direction method of multipliers (ADMM). Extensive experiments on real infrared remote sensing datasets demonstrate that the proposed method achieves superior denoising and restoration performance, exhibiting strong robustness and practical applicability.

1. Introduction

Cryogenically cooled infrared detectors often suffer from image degradation during prolonged on-orbit operation due to non-uniform response, electronic noise, and fluctuations in the temperature control accuracy of the cryocooler. These factors can lead to image blurring, reduced contrast, stripe noise, and random noise, ultimately impairing the system’s ability to detect weak targets and limiting its applicability in high-precision remote sensing tasks. Among these degradations, stripe noise is a particularly prevalent and non-negligible artifact in image restoration. Currently, approaches to infrared image deblurring and destriping can be broadly categorized into two groups: traditional model-based methods and deep learning-based techniques.

For single-frame image destriping, traditional methods such as Fourier transform, wavelet decomposition, moment matching, and histogram matching have been widely adopted [1,2,3,4]. However, these approaches often suffer from limited adaptability and weak robustness when applied to complex remote sensing imagery. To address these limitations, Gadallah [5] proposed a hybrid method that integrates statistical matching and filtering, yet it remains prone to over-smoothing and artifact generation. In recent years, variational models have gained attention due to their strong interpretability. Representative methods include total variation (TV) [6], unified TV (UTV) [7], and MAP models incorporating Huber–Markov priors [8]. Wang et al. [9] introduced a joint $L_0$ TV regularization with a low-rank tensor prior, while Kim et al. [10] enhanced destriping performance using an ADMM-based least squares framework. Cao et al. [11] incorporated non-local information to construct a non-local TV model. Among low-rank-based approaches, GRLD [12] preserved structural details via graph regularization and low-rank constraints, and Chang et al. [13] developed a transform-domain low-rank decomposition framework to handle non-periodic stripes. Despite continued improvements in accuracy and robustness, preserving edge and fine-detail structures remains a challenging task. With the rapid development of deep learning techniques, Kuang et al. [14] first introduced a convolutional neural network (CNN) for stripe noise removal. Xiao et al. [15] further improved the approach by incorporating a residual learning mechanism into the CNN framework. To address limitations in reconstruction accuracy, Yuan et al. [16] proposed an asymmetric sampling correction network capable of effectively separating stripe artifacts from image content. Wang et al. [17] designed Translution-SNet, which integrates CNN and Transformer architectures for enhanced destriping performance. Additionally, Yang et al. [18] introduced DestripeCycleGAN, an unsupervised destriping framework for single-frame infrared images. While deep learning-based methods demonstrate strong feature extraction and modeling capabilities, their performance is often limited by the diversity and availability of training data, resulting in reduced generalization across different imaging conditions and sensor platforms.

Single-image deblurring techniques have achieved significant progress in recent years [19,20]. These methods can be categorized into blind and non-blind deblurring, depending on whether the blur kernel is known. This work focuses on the latter. Classic blind deblurring algorithms, such as Wiener filtering [21] and the Richardson–Lucy (RL) algorithm [22], remain widely used due to their simplicity and effectiveness; however, they often introduce ringing artifacts near strong edges. To address this issue, Levin et al. [23] incorporated sparse derivatives as priors. Ben-Ezra et al. [24] combined the RL algorithm with the Lucas–Kanade optical flow method for motion deblurring. Krishnan et al. [25] proposed a sparse distribution model based on normalized high-frequency components. Yuan et al. [16] leveraged paired blurry and noisy images to enhance low-light deblurring performance. In the context of remote sensing, Cao et al. [26] improved blur kernel estimation using a modified dark channel prior. Lim et al. [27] integrated L0-norm-based intensity priors with dark channel priors and L2-norm regularization to better preserve texture and detail. Liang et al. [28] introduced a local gradient product (LGP) prior based on the inner product of clear image gradients, further improving deblurring accuracy. In recent years, deep convolutional neural networks (CNNs) have been widely applied in image deblurring. Ghosh and Gong et al. [29,30] were among the first to use CNNs to learn the mapping between degraded images and blur kernels, enabling automatic blind deconvolution and image restoration. Fu et al. [31] proposed a two-stage edge-aware deep network inspired by the human visual system’s sensitivity to edges, significantly enhancing edge sharpness. To improve performance in dynamic scenes, some studies have integrated event-based data with neural radiance fields (NeRFs). However, training such models remains challenging due to motion blur interference. To address this, E2NeRF [32] combines motion structure with event-guided deblurring models, though its supervision is limited to the exposure period. EvDeblurNeRF [33] introduces a novel prior based on event double integration, effectively improving deblurring accuracy. Chen et al. [34] proposed a residual-based two-stage framework (TRMD) that leverages rich motion cues from event encoding to convert blurry inputs into sharp image sequences. Overall, deep learning methods exhibit strong performance in image deblurring. However, their effectiveness heavily depends on the diversity and quality of training datasets, and their generalization capability can degrade significantly in domain-shift scenarios.

This work focuses on blind image deblurring under structured stripe noise. Chang et al. [35] proposed a unified optimization framework for simultaneous image denoising and deblurring; however, residual stripes still interfere with accurate kernel estimation. Cao et al. [36] introduced a staged image restoration framework that jointly estimates image content and residual stripe noise, enhancing both restoration accuracy and stability. Furthermore, Zhang et al. [37] developed a joint destriping and deblurring model and systematically compared its performance with conventional step-wise approaches. Experimental results demonstrate that joint modeling offers significant advantages in preserving structural details and suppressing noise-induced artifacts.

In this paper, we propose a unified three-stage image restoration framework that simultaneously addresses stripe removal, blur kernel estimation, and non-blind deblurring, aiming to recover clear images from stripe-contaminated and blurred observations. Specifically, the image is first processed using a wavelet transform. Stripe noise predominantly appears in the vertical and approximation sub-bands. To remove it while preserving image structures, a structure tensor-based method is introduced, which exploits the sparsity and directionality of stripe noise. This strategy enhances edge preservation and detail retention during the denoising stage. After stripe removal, an inverse wavelet transform reconstructs the denoised image. During the blur kernel estimation phase, we incorporate a directional fidelity term aligned with the stripe orientation, as well as a stripe residual constraint, both of which help suppress the negative influence of residual noise and improve the accuracy of the estimated blur kernel. Finally, in the non-blind image deblurring stage, we propose a novel Wiener–COS hybrid filtering model (WCOB). This model effectively reduces ringing artifacts and visual distortion, thus significantly enhancing the quality of the restored image. The main contributions of this work are summarized as follows:

(1) A unified variational model is developed for joint deblurring and destriping, where the influence of stripe residuals on kernel estimation is explicitly addressed.

(2) An adaptive edge-preserving destriping constraint based on the structure tensor is proposed to effectively retain image edges and fine details. In addition, a fidelity term based on the directional gradient of stripes is introduced to enhance blur kernel estimation accuracy by suppressing stripe-induced noise within the kernel.

(3) During the non-blind restoration stage, a WCOB-based hybrid filtering model is established to reduce ringing artifacts and improve restoration quality.

The overall workflow of the proposed three-stage joint image restoration framework is illustrated in Figure 1. The remainder of this paper is organized as follows. Section 2 presents the image degradation model and the proposed restoration framework, including an analysis of stripe noise characteristics, ringing suppression strategies during deblurring, and the development of an alternating minimization algorithm based on the proposed model. Section 3 provides extensive experimental validation of the method’s restoration performance and discusses the selection of key parameters. Finally, Section 5 concludes the paper.

2. Materials and Methods

According to the imaging chain, infrared images are subject to degradation caused by the optical system, atmospheric turbulence, and platform motion, which collectively lead to image blurring. In addition, due to non-uniformities in the readout circuitry, stripe noise often appears in the form of column- or row-wise structured artifacts. Typically, such degraded images can be modeled as follows:

$$B=I\otimes K+S$$

(1)

where I denotes the underlying clean image with low-rank properties, B represents the observed degraded image, and S encompasses both stripe noise and random noise. K denotes the optical point spread function (PSF).

Based on the theoretical modeling of infrared imaging and the degradation equation in Equation (1), this work formulates a blind deblurring model under a variational framework by incorporating an enhanced sparsity prior. An efficient optimization algorithm is developed accordingly, and the objective function is defined as follows:

$$\begin{array}{cc}\hfill arg\underset{I,S,K}{min}& ( \frac{1}{2}{\Vert I\otimes K+S-B\Vert }_2^2+{\displaystyle \frac{{\rho }_1}{2}}\Vert {\nabla }_x{(I\otimes K-B)\Vert }_2^2+{\rho }_2{\Vert \nabla I\Vert }_1+{\displaystyle \frac{{\rho }_5}{2}}{\Vert L\otimes K\Vert }_2^2\hfill \\ \hfill & +{\rho }_6{\Vert \nabla K\Vert }_2^2+R_s\left(S\right))\hfill \end{array}$$

(2)

where ${\rho }_1$, ${\rho }_2$, ${\rho }_5$ and ${\rho }_6$ are weighting parameters. The first term represents the data fidelity term commonly used in deblurring models. The second term, proposed in this work, aims to align the stripe-free image I and the blurred image B in the horizontal direction as closely as possible, thereby minimizing the impact of stripe noise S. The third term promotes smoothness of the reconstructed image in both horizontal and vertical directions. The fourth term is a fidelity constraint on the blur kernel K, where L denotes a weight matrix designed to encourage kernel smoothness. The seventh term suppresses noise within the blur kernel. The term $R_s\left(S\right)$ represents the objective function for stripe noise removal, and its detailed formulation is given in Equation (13).

About L, we first define the two-dimensional Laplacian (PSF):

$$L_{\mathrm{pc}}=\left[\begin{array}{ccc}0& -1& 0\\ -1& 4& -1\\ 0& -1& 0\end{array}\right]$$

(3)

Then we convert the PSF to OTF (frequency response):

$${\mathcal{F}}_{\mathrm{L}}(u,v)=\mathrm{OTF}\left(L_{\mathrm{pc}},M\times N\right)$$

(4)

Finally, the squared amplitude of the Laplacian in the frequency domain is calculated, which is used as our weight coefficient L:

$$L={\left|{\mathcal{F}}_L(u,v)\right|}^2={\mathcal{F}}_L(u,v)·{\mathcal{F}}_L^{*}(u,v)$$

(5)

where $M\times N$ denotes the size of the image, ${\mathcal{F}}_{\mathrm{L}}(u,v)$ represents the response of the 2D Laplacian kernel $L_{pc}$ at the frequency point $(u,v)$, and ${\mathcal{F}}_{\mathrm{L}}^{*}(u,v)$ denotes the complex conjugate.

2.1. Estimation of Stripe Noise S

To begin with, a wavelet transform is applied to decompose the stripe-contaminated image:

$$D_1=c{A}_1+c{H}_1+c{V}_1+c{D}_1$$

(6)

$$c{A}_{n-1}=c{A}_n+c{H}_n+c{V}_n+c{D}_n$$

(7)

where D denotes the original observed image, and $c{A}_n$, $c{H}_n$, $c{V}_n$ represent the approximation (low-frequency) subband, horizontal high-frequency subband, vertical high-frequency subband, and diagonal high-frequency subband obtained at the n-th decomposition level, respectively, where n denotes the wavelet decomposition level (theoretically any positive integer). In the methodological description, a general multi-level decomposition is presented to facilitate theoretical derivation; however, in practical implementation and all experiments, a single-level wavelet decomposition ($n=1$) was employed as a preprocessing step. Empirical results show that a single-level decomposition effectively concentrates the stripe energy in the vertical and approximation subbands, thereby facilitating subsequent stripe estimation and restoration based on the structure tensor. Moreover, the single-level design achieves a favorable trade-off between edge structure preservation and computational efficiency.

The effect of the wavelet decomposition level on stripe extraction and edge preservation was investigated experimentally. For $n=1$, the stripe energy is primarily concentrated in the vertical subband, with minimal impact on edge preservation. For $n=2$, a slight advantage can be observed in certain extreme low-frequency stripe scenarios, but at the cost of increased computational overhead. When $n\ge 3$, image details may be excessively dispersed across deeper subbands, resulting in edge smoothing. Based on these observations, a decomposition level of $n=1$ was consistently adopted in all experiments to achieve a balance between stripe removal performance and computational efficiency. As shown in Figure 2, stripe noise is primarily concentrated in the vertical and approximation components.

Based on a variational framework, this paper focuses on extracting stripe-related components from both the vertical and approximation subbands. However, conventional destriping algorithms often struggle to distinguish between noise and image edge details, which can lead to blurring of image edges while suppressing noise, thereby degrading visual quality. To address this issue, an adaptive edge-preserving operator based on the structure tensor is proposed. This operator constructs a local gradient distribution tensor matrix to characterize the image structure:

$$J=\left[\begin{array}{cc}{g}_x^2& g_x{g}_y\\ g_x{g}_y& g_y^2\end{array}\right]$$

(8)

Among them, $g_x$ and $g_y$ denote the horizontal and vertical gradients of the input image I. The eigenvalues of the matrix ${\lambda }_1$ and ${\lambda }_2$ of the matrix represent the edge characteristics of the image. In edge regions, ${\lambda }_1$ is much greater than ${\lambda }_2$, while in flat regions, ${\lambda }_1\approx {\lambda }_2$. A weighting operator is constructed based on the minimum eigenvalue:

$$\mathsf{\Omega }=1-{\displaystyle \frac{{\lambda }_{min}}{max\left({\lambda }_{min}\right)}}$$

(9)

Among them,

$${\lambda }_{min}={\displaystyle \frac{1}{2}}\left(tr\left(\mathbf{J}\right)-\sqrt{{tr}^2\left(\mathbf{J}\right)-4det\left(\mathbf{J}\right)}\right)$$

(10)

where $tr\left(J\right)$ denotes the trace of the matrix (the sum of its diagonal elements), and $det\left(J\right)$ represents the determinant of the matrix. In this work, a vectorized acceleration approach is adopted, enabling parallel computation of eigenvalues through full matrix operations without the need for iteration loops. This allows for the efficient computation of the edge tensor matrix.

To further clarify the effectiveness of the structure tensor for edge preservation and stripe suppression, we provide the following theoretical justification. The structure tensor describes the statistical distribution of gradient orientations within a local neighborhood, where its eigenvalues ${\lambda }_1\ge {\lambda }_2\ge 0$ quantify the energy along the principal and secondary directions. In natural images, true edges produce strong gradients primarily in the direction orthogonal to the edge, yielding a highly anisotropic structure characterized by ${\lambda }_1\gg {\lambda }_2$. The dominant eigenvector further indicates the edge orientation. In contrast, sensor-induced stripes, although directionally consistent, differ in two key aspects; their orientation is globally uniform across the image, and they typically manifest as low-amplitude, narrow-band periodic disturbances.

To better distinguish these patterns, a coherence measure is introduced to quantify the degree of local anisotropy:

$$C={\displaystyle \frac{{\lambda }_1-{\lambda }_2}{{\lambda }_1+{\lambda }_2+\epsilon }}$$

(11)

where $\epsilon$ is a small constant. The coherence measure facilitates clearer discrimination between true structural features and noise. Although stripe regions also exhibit high coherence, their dominant orientations coincide with the known stripe direction, whereas genuine image edges vary with scene content. Based on this property, the proposed method combines the coherence C with the prior stripe direction to construct an adaptive weighting function. As a result, real edges are preserved due to their large eigenvalue disparity and orientations inconsistent with the stripe direction, stripe components are suppressed because their orientations align with the known stripe direction, and flat regions remain smooth since both ${\lambda }_1$ and ${\lambda }_2$ are small. Compared with traditional TV or bilateral filtering, which rely mainly on gradient magnitude, the structure tensor exploits both local energy and directional information, offering greater robustness for anisotropic structures and superior capability in separating fixed-direction stripe noise from true edges.

In addition, this study compares several commonly used edge-preserving operators and presents the corresponding processed images. Furthermore, the Edge Preservation Index (EPI) is employed to provide a more intuitive and quantitative comparison of their performance. The calculation method of the EPI is as follows.

$$\mathrm{EPI}={\displaystyle \frac{{\sum }_{p\in \mathsf{\Omega }}\left|\nabla I_{\mathrm{out}}\left(p\right)\right|}{{\sum }_{p\in \mathsf{\Omega }}\left|\nabla I_{\mathrm{ref}}\left(p\right)\right|}}$$

(12)

where $I_{\mathrm{out}}$ denotes the processed image, $I_{\mathrm{ref}}$ represents the reference image, ∇ is the gradient operator, and $\mathsf{\Omega }$ refers to the statistical region, which may correspond to the entire image or only the edge regions, while p denotes the pixel position within $\mathsf{\Omega }$. An EPI value closer to 1 (or higher) indicates superior edge preservation performance. From the Figure 3, both the visual results and the EPI measurements clearly demonstrate that the proposed structure-tensor-based edge-preserving operator outperforms the other methods in terms of edge retention.

During the optimization, the split Bregman iteration method is employed, and three auxiliary variables $d_1$, $d_2$ and $d_3$ are introduced to reformulate the unconstrained optimization problem with respect to the stripe noise S in Equation (2) as a constrained one.

$$Y\left(S\right)=arg\underset{S}{min}\left\{{\mathcal{R}}_s\left(S\right)\right\}=arg\underset{S}{min}\left\{{\rho }_3\Vert d_1{\Vert }_1+{\rho }_4\Vert d_2{\Vert }_1+{\rho }_7{\mathsf{\Omega }}_1\Vert d_3{\Vert }_1\right\}$$

(13)

$$\begin{array}{cc}\hfill \mathrm{s}.\mathrm{t}.& d_1={\nabla }_{y}S,\hfill \\ \hfill & d_2=S,\hfill \\ \hfill & d_3={\nabla }_{x}B-{\nabla }_{x}S.\hfill \end{array}$$

(14)

$d_1$ characterizes the sparsity and smoothness of stripe noise gradients along the vertical direction. $d_2$ reflects the fact that, although some infrared detectors exhibit significant non-uniformity and limited consistency, stripe noise is still sparsely distributed across the entire image. $d_3$ accounts for the degradation of image gradients along the horizontal direction due to stripe noise. Typically, the horizontal gradients of informative image structures are relatively smooth. To preserve such structures, we propose an adaptive edge-preserving operator based on the structure tensor, denoted as ${\mathsf{\Omega }}_1$. This operator assigns lower weights to edge pixels and higher weights to non-edge pixels, thereby enabling adaptive regularization guided by ${\mathsf{\Omega }}_1$ to constrain the image while preserving true structural information.

The convex optimization problem in Equation (13) is further transformed into the augmented Lagrangian function:

$$\begin{array}{cc}\hfill S=\underset{S,d_1,d_2,d_3}{argmin}\{{\displaystyle \frac{1}{2}}\Vert {\nabla }_{y}S-d_1+Q_1{\Vert }_2^2+{\displaystyle \frac{1}{2}}{\Vert S-d_2+Q_2\Vert }_2^2& +{\displaystyle \frac{1}{2}}{\Vert {\nabla }_{x}B-{\nabla }_{x}S-d_3+Q_3\Vert }_2^2\hfill \\ \hfill +{\rho }_2\Vert d_1{\Vert }_1+{\rho }_4\Vert d_2{\Vert }_1+{\rho }_7{\mathsf{\Omega }}_1{\Vert d_3\Vert }_1\}\end{array}$$

(15)

At this stage, Equation (15) can be decomposed into four separate subproblems, which are solved iteratively.

2.1.1. Recover the Stripe Noise S

Equation (16) corresponds to the subproblem for solving S, where $\mathcal{F}$, $\overline{\mathcal{F}}$ and ${\mathcal{F}}^{-1}$ denote the FFT transform, its conjugate, and the inverse transform, respectively. The symbol “·” represents the element-wise matrix multiplication, and ${\nabla }_x=(1,-1)$ and ${\nabla }_y={(1,-1)}^T$.

$$S={\mathcal{F}}^{-1}\left({\displaystyle \frac{\overline{\mathcal{F}}\left({\nabla }_y\right)\mathcal{F}(d_1-Q_1)+\mathcal{F}(d_2-Q_2)+\overline{\mathcal{F}}\left({\nabla }_x\right)·\mathcal{F}(d_3-Q_3)}{\overline{\mathcal{F}}\left({\nabla }_y\right)·\mathcal{F}\left({\nabla }_y\right)+1+\overline{\mathcal{F}}\left({\nabla }_x\right)·\mathcal{F}\left({\nabla }_x\right)}}\right)$$

(16)

2.1.2. About $d_1$, $d_2$, $d_3$

$$d_1=\underset{d_1}{argmin}\left\{{\displaystyle \frac{1}{2}}{∥{\nabla }_{y}S-d_1+Q_1∥}_2^2+{\rho }_3{∥d_1∥}_1\right\}$$

(17)

By introducing the shrinkage operator shrink, the solution can be obtained as follows:

$$d_1^{t+1}=max\left(\left|{\nabla }_{y}S+Q_1\right|-2{\rho }_3,0\right)·sign({\nabla }_{y}S+Q_1)$$

(18)

Similarly,

$$d_2^{t+1}=max\left(\left|S+Q_2\right|-2{\rho }_4,0\right)·sign(S+Q_2)$$

(19)

$$\begin{array}{cc}\hfill d_3^{t+1}& =max\left\{\left|{\nabla }_{x}B-{\nabla }_{x}S+Q_3\right|-2{\rho }_7{\mathsf{\Omega }}_1,0\right\}·\hfill \\ \hfill & sign\left({\nabla }_{x}B-{\nabla }_{x}S\right)\hfill \end{array}$$

(20)

The Lagrange multipliers are updated iteratively as follows:

$$Q_1^{t+1}=Q_1^t+{\nabla }_{y}S-d_1^{t+1}$$

(21)

$$Q_2^{t+1}=Q_2^t+S-d_2^{t+1}$$

(22)

$$Q_3^{t+1}=Q_3^t+{\nabla }_{x}B-{\nabla }_{x}S-d_3^{t+1}$$

(23)

After solving for the stripe noise S through the above process, the denoised image $I_{\mathrm{destriped}}$ is as follows:

$$I_{\mathrm{destriped}}=B-S$$

(24)

Here, we compare the destriping performance of the test images that contain both stripe noise and blur using the methods in [10,18,38,39], and our proposed approach. As shown in the results in Figure 4, our method demonstrates superior detail preservation after stripe removal compared to the SLDR and ADOM methods.

2.2. Estimation of the Blur Kernel K

Due to the influence of stripe noise on the accuracy of the image blur kernel estimation, we first remove the stripe noise before performing image deblurring. As illustrated in Figure 5, from the comparison between (c) and (d), it is evident that stripe noise significantly affects the X-direction derivative. In contrast, the comparison between (e) and (f) indicates that stripe noise has a minimal impact on the gradient in the Y direction. Ideally, without the presence of stripe noise, the X-direction derivatives of the ideal and degraded images should be consistent. However, if blind deblurring is applied directly without removing stripes, the estimated blur kernel shape is shown in (h). Comparing (g) and (h), it is clear that the presence of stripe noise alters the kernel shape along the stripe direction, leading to inaccurate kernel estimation. To address this issue, we construct a multi-scale Gaussian space during the blur kernel estimation process and simultaneously solve for the low-rank image I and the blur kernel K.

2.2.1. Estimation of the Low-Rank Image I

We write the equation of the objective function for I as follows:

$$\begin{array}{cc}\hfill I=arg\underset{I}{min}\{& {\displaystyle \frac{1}{2}}{\Vert I\otimes K+S-B\Vert }_2^2+{\displaystyle \frac{{\rho }_1}{2}}{\Vert {\nabla }_x(I\otimes K-B)\Vert }_2^2\hfill \\ \hfill & +{\rho }_2{\mathsf{\Omega }}_1{\Vert \nabla I\Vert }_1\}\hfill \end{array}$$

(25)

Similarly, by introducing the auxiliary variable $d_4$, we reformulate Equation (25) into the following expression for an iterative solution:

$$\begin{array}{cc}\hfill I=arg\underset{I}{min}& \left\{{\displaystyle \frac{1}{2}}{\Vert I\otimes K+S-B\Vert }_2^2+{\displaystyle \frac{{\rho }_1}{2}}{\Vert {\nabla }_x(I\otimes K-B)\Vert }_2^2\right.\hfill \\ \hfill & +{\rho }_2{\mathsf{\Omega }}_1{\Vert d_4\Vert }_1\}\hfill \end{array}$$

(26)

$$d_4=arg\underset{d_4}{min}\left\{{\displaystyle \frac{1}{2}}\Vert {\nabla }_{y}I-d_4+Q_4{\Vert }_2^2+{\rho }_2{\mathsf{\Omega }}_1{\Vert d_4\Vert }_0\right\}$$

(27)

The update rule for $d_4$ is given as follows:

$$d_4^{t+1}=max\left\{\left|{\nabla }_{y}I+Q_4\right|-2{\rho }_2{\mathsf{\Omega }}_1,0\right\}·sign({\nabla }_{y}I+Q_4)$$

(28)

$$Q_4^{t+1}=Q_4^t+{\nabla }_{y}I-d_4^{t+1}$$

(29)

2.2.2. Estimation of the Blur Kernel K

The estimation of the blur kernel K is also formulated as a least squares problem. In this work, we incorporate the Laplacian operator L into the gradient domain and employ a fast deblurring method to optimize K. The objective function for K is thus defined as follows:

$$\begin{array}{cc}\hfill K=arg\underset{K}{min}& \{{\displaystyle \frac{{\rho }_1}{2}}{∥\nabla \left(I\otimes K+S-B\right)∥}_2^2+\hfill \\ \hfill & {\displaystyle \frac{{\rho }_5}{2}}{∥L\otimes K∥}_2^2+{\rho }_6{∥\nabla K∥}_2^2\}\hfill \end{array}$$

(30)

By applying the FFT to Equation (30), the solution can be obtained as Equation (31).

$$K={\mathcal{F}}^{-1}\left({\displaystyle \frac{{\rho }_1\overline{\mathcal{F}}\left(I\right)·\overline{\mathcal{F}}(\nabla )·\mathcal{F}(B-S)}{{\rho }_5\overline{\mathcal{F}}\left(L\right)·\mathcal{F}\left(L\right)+{\rho }_1\overline{\mathcal{F}}\left(I\right)·\overline{\mathcal{F}}(\nabla )·\mathcal{F}(\nabla )·\mathcal{F}\left(I\right)+{\rho }_6\overline{\mathcal{F}}(\nabla )·\mathcal{F}(\nabla )}}\right)$$

(31)

During the blur kernel estimation process, since the PSF of most remote sensing images closely approximates a Gaussian distribution, the kernel is initialized with a Gaussian model to accelerate convergence. Here, L denotes the Laplacian operator introduced in this work, which effectively suppresses internal noise within the blur kernel and improves the accuracy of kernel estimation.

2.3. Estimation of the Clear Image I

After estimating the blur kernel, the next step is the non-blind image restoration process. Although Wiener filtering has achieved significant success in non-blind image restoration, its performance degrades in the presence of noise and PSF estimation errors, often introducing pronounced ringing artifacts in smooth regions and around edges. To address this limitation, we propose a hybrid filtering approach, the Wiener-Cosine (WCOB) filter, which synergistically combines the strengths of both filters to achieve a more robust restoration.

The Wiener filter is optimal in the mean-square error sense but is sensitive to model inaccuracies. Its frequency response is given by:

$$iH{H}_{\mathrm{wiener}}(u,v)={\displaystyle \frac{H^{*}(u,v)}{{\left|H(u,v)\right|}^2+K}}$$

(32)

where $H(u,v)$ denotes the frequency domain representation of the degradation function PSF, and K is the estimated ratio of the noise power spectrum to the original signal power spectrum.

Conversely, the Cosine filter, defined by its smooth roll-off, is particularly effective at suppressing Gibbs phenomena (ringing artifacts) caused by frequency domain truncation. Its response is defined as follows:

$$iH{H}_{cos}(u,v)=cos\left(\pi ·{\displaystyle \frac{H(u,v)}{2}}\right)·\mathrm{rectpupil}\left({\displaystyle \frac{H(u,v)}{2}}\right)$$

(33)

$$y=\mathrm{rectpupil}\left(x\right)=\left\{\begin{array}{cc}1,\hfill & \mathrm{if}\left|x\right|<0.5,\hfill \\ 0,\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

(34)

where $H(u,v)$ represents the normalized radial distance from the center of the frequency domain, ensuring the filter’s isotropic property. This design creates a smooth transition band that effectively tapers the frequency response, thereby mitigating ringing.

The proposed WCOB model is centered on an adaptive fusion of the Wiener filter and the Cosine filter. Within the WCOB filtering module, these two filters exhibit complementary characteristics in terms of detail preservation and ringing-artifact suppression, and they are integrated through a weighted fusion scheme to effectively exploit their respective advantages. The combined frequency response is defined as:

$$iHH(u,v)=\alpha (u,v)·iH{H}_{\mathrm{wiener}}(u,v)+(1-\alpha (u,v))·iH{H}_{cos}(u,v)$$

(35)

where $\alpha (u,v)$ denotes an adaptive weighting coefficient that controls the relative contributions of the Wiener and Cosine filters. The value of $\alpha (u,v)$ is determined based on the overall signal-to-noise ratio (SNR) of the input image. Specifically, when the image SNR is relatively high, a larger value of $\alpha (u,v)$ is selected to strengthen the contribution of the Wiener filter, thereby enabling more effective recovery of image structures and fine details. Conversely, when the image SNR is low and the risk of noise amplification and ringing artifacts increases, a smaller value of $\alpha (u,v)$ is adopted to assign a higher relative weight to the Cosine filter, which helps suppress noise and ringing artifacts introduced during deconvolution and improves the overall stability and robustness of the reconstruction. This SNR-guided global fusion strategy allows WCOB to flexibly balance detail restoration and artifact suppression under different degradation conditions, overcoming the limitations of using either filter alone and yielding more stable and reliable restoration results.

To avoid ambiguity in the restoration stage, we explicitly denote the input of the non-blind deblurring module as $I_{destriped}$. After the destriping procedure removes the vertical stripe component S from the observed image B, the intermediate image $I_{destriped}=B-S$ serves as a cleaner approximation of the latent sharp image. The restored image is thus obtained as follows:

$$I(x,y)=\mathrm{real}\left\{{\mathcal{F}}^{-1}(iHH(u,v)·\mathcal{F}\left\{I_{\mathrm{destriped}}\right\}(u,v))\right\}$$

(36)

where $iHH(u,v)$ represents a frequency-domain filter and should not be further transformed by F. Using $I_{destriped}$ as the input ensures that the subsequent deblurring focuses solely on the optical blur while preventing the stripe component from interfering with kernel inversion.

To evaluate the effectiveness of the proposed ringing suppression method, non-blind restoration was performed on images degraded by known blur kernels and stripe noise, with results illustrated by visual comparisons and signal plots.

As shown in Figure 6, (a) depicts the original image, (b) shows the restoration result using Wiener filtering, and (c) presents the restoration outcome of the proposed combined filtering method. Figure 7 illustrate the signal profiles of the original and restored images along row X and column X, respectively. By examining the magnified regions and comparing the original signals with the restored ones, it is evident from the local comparisons in (b) and (c) that Wiener filtering exhibits more pronounced edge truncation effects near boundaries.

In Figure 7a,b, the green, blue, and red curves represent the signals of the Wiener filter, the combined filter, and the original image, respectively. At boundary regions, the green curve is significantly higher than the red curve, while the blue curve lies between them, demonstrating that the proposed method effectively suppresses ringing artifacts to a large extent.

An image pyramid is used to progressively refine the blur kernel from coarse to fine scales. Once the kernel is estimated, non-blind restoration is applied to obtain the final restored image. The main iterative steps are summarized in Algorithm 1.

Algorithm 1: Proposed destriping and deblurring algorithm.

Input: Blurred image with stripes B, parameters $\beta$, $\rho$, $\mathsf{\Omega }$, L, maximum iterations $i_{max}$

Output: Estimated blur kernel K, restored image I

1. Estimate stripe component S based on Equation (15).

2. For $i=1$ to $i_{max}$ do.

3.    Compute the edge-preserving operator using Equation (9).

4.    Initialize ${\rho }_3\leftarrow {\rho }_{3init}$.

5.    While ${\rho }_3<{\rho }_{3max}$ do.

6.       Update $d_1$ using Equation (18).

7.       Initialize ${\rho }_4\leftarrow {\rho }_{4init}$.

8.       While ${\rho }_4<{\rho }_{4max}$ do.

9.          Update $d_2$ using Equation (19).

10.          Initialize ${\rho }_7\leftarrow {\rho }_{7init}$.

11.          While ${\rho }_7<{\rho }_{7max}$ do.

12.             Update $d_3$ using Equation (20) and the edge-preserving operator.

13.             ${\rho }_7\leftarrow 2{\rho }_7$.

14.          End While.

15.          ${\rho }_4\leftarrow 2{\rho }_4$.

16.       End While.

17.       ${\rho }_3\leftarrow 2{\rho }_3$.

18.    End While.

19. End For.

20. Update blur kernel K under stripe constraint using Equation (30).

21. Update $d_4$ using Equation (28) in Equation (26).

22. Update clear image I based on Equation (36).

3. Experiment and Analysis

3.1. Experimental Setup

3.1.1. Environment and Parameter Selection

In this study, we selected publicly available infrared-band datasets, including data from the Jilin-1 satellite, thermal infrared spectrometer (TIS) data from the SDGSAT-1 satellite [40,41,42], as well as a thermal infrared image from the MODIS RSI dataset [43]. These images were artificially degraded by introducing known convolutional blur and stripe noise, thereby establishing reference-based datasets for quantitative evaluation. To ensure fairness and reproducibility in testing, the clean images were first rescaled to 8-bit format prior to data generation.

Choosing appropriate parameters is crucial for the proposed model in this study, as the algorithm involves seven regularization parameters. After extensive empirical validation and comparing the effects of fine-step adjustments for each parameter, the parameters ${\rho }_4$ and ${\rho }_7$ were set to 0.02. To accommodate varying noise intensities, the parameter ${\rho }_3$ was tuned within the range of [0.1, 0.2]. The Gaussian smoothing scale employed in the structure tensor for the edge-preserving operator was fixed at 1.5. During both blur kernel estimation and image restoration, the regularization coefficients ${\rho }_1$ and ${\rho }_2$ were set to 0.01 and $4\times {10}^{-3}$, respectively. Furthermore, by adjusting the weighting terms related to kernel estimation, the parameters ${\rho }_5$ and ${\rho }_6$ were both assigned a value of 1 to optimize blur kernel recovery performance. All experiments were conducted on a personal computer equipped with an Intel Core i7 processor (2.20 GHz) and 16 GB RAM. The proposed optimization-based method was implemented in MATLAB (v2020) and executed entirely on the CPU without GPU acceleration or any parallel-computing architectures. The deep-learning baseline methods followed their original implementations in PyCharm 2024.3 under the Python (v3.9) environment, which rely on GPU-accelerated deep-learning frameworks for network inference.

3.1.2. Evaluation Indexes

Here, a brief introduction is given to the evaluation indicators and calculation methods used in this article. The reference evaluation indexes structural similarity (SSIM) and peak signal-to-noise ratio (PSNR) and are defined as follows:

$$\mathrm{SSIM}(x,y)={\displaystyle \frac{(2{\mu }_x{\mu }_y+c_1)(2{\sigma }_{xy}+c_2)}{({\mu }_x^2+{\mu }_y^2+c_1)({\sigma }_x^2+{\sigma }_y^2+c_2)}}$$

(37)

where ${\mu }_x$ and ${\mu }_y$ denote the mean intensities of the current image X and the reference image Y, respectively; ${\sigma }_x^2$ and ${\sigma }_y^2$ represent their respective variances; ${\sigma }_{xy}$ denotes the covariance between X and Y; and $c_1$ and $c_2$ are small constants introduced to stabilize the division.

$$\mathrm{PSNR}(I,K)=10{log}_{10}\left({\displaystyle \frac{{(2^B-1)}^2}{\frac{1}{MN}{\sum }_{i=1}^M{\sum }_{j=1}^N{[I(i,j)-K(i,j)]}^2}}\right)\left(\mathrm{dB}\right)$$

(38)

where MSE represents the mean square error and m is the number of bits per pixel. The higher the values of SSIM and PSNR, the better the image restoration.

The no-reference metrics Natural Image Quality Evaluator (NIQE), image Contrast Value (ICV) [8] and mean relative deviation (MRD) [44] are defined as follows:

$$\mathrm{NIQE}=\sqrt{{\left({\mathbf{v}}_{\mathrm{test}}-{\mathbf{v}}_{\mathrm{natural}}\right)}^T·{\mathsf{\Sigma }}_{\mathrm{natural}}^{-1}·\left({\mathbf{v}}_{\mathrm{test}}-{\mathbf{v}}_{\mathrm{natural}}\right)}$$

(39)

In this model, $v_{test}$ denotes the statistical feature vector extracted from the test image, $v_{natural}$ is the mean feature vector learned from a high-quality natural image database, and $\mathsf{\Sigma }\mathrm{natural}$ represents the covariance matrix of natural image features, capturing their statistical dependencies. The NIQE score is computed as a weighted Euclidean distance between $v_{test}$ and $v_{natural}$, where the weighting matrix is the inverse covariance matrix $\mathsf{\Sigma }{\mathrm{natural}}^{-1}$.

$$\mathrm{ICV}={\displaystyle \frac{{\sigma }_{\mathrm{horizontal}}}{{\sigma }_{\mathrm{vertical}}}}$$

(40)

where ${\sigma }_{\mathrm{horizontal}}$ represents the standard deviation of the horizontal gradients in the image, ${\sigma }_{\mathrm{vertical}}$ denotes the standard deviation of the vertical gradients, which is highly sensitive to stripe noise. The ratio of these two terms effectively quantifies both the suppression of stripe noise and the preservation of natural image textures. The higher the ICV, the better the image restoration.

$$\mathrm{MRD}={\displaystyle \frac{1}{M\times N}}\sum _{i=1}^{M\times N}{\displaystyle \frac{\left|z_i-g_i\right|}{g_i}}\times 100\%$$

(41)

where $g_i$ and $z_i$ represent the pixel values of the original image and the denoised image, respectively. $M\times N$ is the size of the selected image area. MRD can reflect the image retention ability of areas less affected by stripes, and the smaller the values of NIQE and MRD, the better the image retention ability.

To assess whether the performance advantages of the proposed method over other comparative methods are statistically significant, this study conducts significance tests on per-image evaluation metrics. Considering the distinct statistical characteristics of different evaluation metrics, paired t-tests and Wilcoxon signed-rank tests are employed accordingly.

(1)

Paired t-Test

SSIM and PSNR are continuous measures that generally exhibit approximately normal distributions across multiple test samples. Therefore, a two-sided paired t-test was applied to determine whether the proposed method yields statistically significant improvements compared with each baseline method. For each test image, the performance difference is defined as:

$$d_i=x_i-y_i,i=1,2,\dots ,N$$

(42)

where $x_i$ and $y_i$ denote the metric values of the proposed method and a competing method, respectively.

The mean and standard deviation of the paired differences are given by:

$$\overline{d}={\displaystyle \frac{1}{N}}\sum _{i=1}^N{d}_i$$

(43)

$$s_d=\sqrt{{\displaystyle \frac{1}{N-1}}\sum _{i=1}^N{(d_i-\overline{d})}^2}$$

(44)

The test statistic is defined as:

$$t={\displaystyle \frac{\overline{d}}{s_d/\sqrt{N}}}$$

(45)

which follows a t-distribution with $N-1$ degrees of freedom. A p-value below 0.05 indicates that the performance improvement of the proposed method is statistically significant.

(2)

Paired t-Test

NIQE, ICV and MRD are no-reference quality metrics that do not necessarily follow a normal distribution and typically exhibit relatively high variance across different scenes. For this reason, the nonparametric Wilcoxon signed-rank test was adopted.

Given paired differences $d_i=x_i-yi$, samples with $d_i=0$ are excluded. The absolute differences are ranked, yielding the positive and negative rank sums:

$$W^{+}=\sum _{d_i>0}{R}_i,W^{-}=\sum _{d_i<0}{R}_i.$$

(46)

where $R_i$ denotes the rank of $|d_i|$

The test statistic is:

$$W=min(W^{+},W^{-}).$$

(47)

A two-sided p-value is computed based on the distribution of W. A value of $p<0.05$ indicates a statistically significant difference.

All tests were performed in a paired manner to ensure that each image is compared only against its own counterparts under different methods, thereby eliminating bias introduced by scene-dependent variations.

3.2. Reference-Based Image Data Experiments

Due to the large size of individual remote sensing images, each selected image was cropped to a region of $800\times 800$ pixels for experimental evaluation. To better visualize the restoration performance, the processed results were locally enlarged. The selected reference images and the corresponding simulated datasets are shown in Figure 8 and Figure 9, respectively. Both qualitative and quantitative assessments were conducted to evaluate the quality of the restored images. The qualitative evaluation includes visual comparison and analysis of column-wise mean profiles. Figure 10a shows the blur kernel used to degrade the image, where a Gaussian kernel with a variance of 2 was applied.

For quantitative evaluation, since the simulated experiments are conducted by introducing artificial blur and noise to real ground-truth images, several full-reference quality metrics are adopted, including Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) [45]. PSNR reflects pixel-level intensity differences, whereas SSIM assesses perceptual structural similarity by comparing local intensity patterns between the restored and ground-truth images. In addition, the no-reference Natural Image Quality Evaluator (NIQE) [46] is employed as a complementary metric to evaluate perceptual quality without relying on ground truth. Higher PSNR and SSIM values correspond to better reconstruction performance, while lower NIQE values indicate higher perceptual quality. Accordingly, in the comparative metric

Table 1. Average quality evaluation results on reference dataset (complex scene).

Method	SSIM	PSNR	NIQE/dB
LRSID+AMRN	0.7876	24.91	5.429
ADOM+AMRN	0.8922	26.68	5.032
LRSID+LGP	0.8295	25.65	5.724
ADOM+LGP	0.9280	27.37	5.606
ADOM+SCGTV	0.8883	25.96	5.299
BSR_GLKM	0.9102	28.68	4.382
RBDS	0.9292	27.43	6.732
De_GANv2	0.7297	20.82	5.700
SLDR_eNeRf	0.8885	29.68	6.622
Ours	0.9565	30.36	4.372

and

Table 2. Average quality evaluation results on reference dataset (flat scene).

Method	SSIM	PSNR	NIQE/dB
LRSID+AMRN	0.6439	22.61	6.263
ADOM+AMRN	0.7777	24.06	6.750
LRSID+LGP	0.6260	22.27	6.732
ADOM+LGP	0.7764	24.16	6.495
ADOM+SCGTV	0.7632	24.14	5.904
BSR_GLKM	0.8497	24.38	5.648
RBDS	0.7816	24.11	7.972
De_GANv2	0.7395	22.45	7.021
SLDR_eNeRf	0.8056	28.34	8.371
Ours	0.8665	28.79	5.498

, the best results are highlighted in bold for clarity.

As shown in Figure 9, the selected images include scenes containing land, ocean and buildings. Each clean image is degraded by applying Gaussian blur with a variance of 2, followed by the addition of random stripe-like noise in the range of [−40, 40], affecting approximately 16% of the total pixels, thereby generating the final degraded dataset. Following a comprehensive review of recent literature, this study selects a set of representative and state-of-the-art methods that are closely related to the proposed approach for comparative evaluation. Due to the scarcity of traditional model-based algorithms that simultaneously address both stripe noise removal and image deblurring, the comparison includes methods that either jointly consider both tasks or represent recent advances in each domain. Specifically, we include both integrated approaches and combined schemes that pair advanced destriping and deblurring techniques to form effective baselines. The compared methods include LRSID [38]+AMRN [47], ADOM [10]+AMRN, LRSID+LGP [28], ADOM+LGP, ADOM+SCGTV [48], SelfBSR [49]+GLKMDeblur [50], RBDS [36], DestripeGAN [18]+PGDN [51], and SLDR [39]+eNeRf [32].

The restoration results obtained by different methods are presented in Figure 11. For each image, a representative region with visually noticeable features is enlarged for detailed comparison. Taking Figure 9a as an example, we focus on the enlarged area covering rooftops and the connecting corridors between buildings. It is evident that, aside from the proposed method, both the LRSID+LGP and ADOM+LGP methods tend to produce darker grayscale outputs. Moreover, the result obtained by LRSID exhibits noticeable residual noise. In contrast, methods such as RBDS, DestripeGAN+PGDN, and SLDR+eNeRf provide more visually pleasing overall results. Notably, the proposed method demonstrates superior performance in suppressing noise and achieves better restoration of architectural details, especially in the highlighted regions. For Figure 9b, the restoration of architectural structures and vegetation is more visually discernible. After processing with several traditional combination-based methods, the fine textures of the trees are noticeably smoothed out, and enlarged residual artifacts appear below the buildings in the outputs of the initial methods. It is also evident that the proposed method occasionally leads to over-brightening in certain areas. Figure 9c corresponds to a nighttime scene, where buildings are located on the left and a river on the right. In the magnified yellow box, it can be observed that although the LRSID-based destriping method is effective, the subsequent deblurring using Attention-driven multi-local residual network (AMRN) results in some degree of visual degradation. Among the compared approaches, SLDR+eNeRf consistently produces better visual quality in this case. Figure 9d depicts a flat ocean surface surrounded by land and vegetation. From this figure, it is apparent that the ADOM-based method performs better on small image patches than on large-scale images. Aside from our proposed method, the other competing approaches leave varying degrees of residual noise unremoved after processing the degraded images. In the magnified yellow boxes, visible residuals can still be seen, and certain coastal regions exhibit noticeable artifacts.

From the enlarged views across these different scenarios, it can be concluded that the proposed method offers superior restoration performance overall. While SLDR+eNeRf shows enhanced capability in reconstructing individual architectural structures, the LRSID combined with various deblurring schemes performs poorly in eliminating stripe noise over flat ocean regions, leaving behind significant stripe-like residuals.

Figure 12 presents the error maps of the original sharp image and the images restored by various denoising and deblurring methods. The results indicate that the proposed method effectively maintains the pixel value differences within approximately 10, demonstrating comparatively superior performance. Figure 13 presents a comparison of the estimated blur kernels obtained by the proposed method and several competing approaches. It can be observed that the four combined methods LRSID+AMRN, ADOM+AMRN, LRSID+LGP and ADOM+LGP fail to fully suppress the ringing artifacts. The estimated kernels produced by these methods exhibit uneven protrusions at the bottom, indicating artifacts introduced during the deblurring process. In contrast, the proposed method, along with five other compared approaches, demonstrates effective suppression of ringing phenomena. Overall, both the proposed method and DestripeGAN+PGDN yield estimated blur kernels that are most consistent with the original ground-truth kernel, highlighting their superior performance in blur kernel recovery.

We further compare the column-wise mean profiles of the restored images to more intuitively reveal the column-wise fluctuations resulting from each method. Specifically, Figure 10a presents the column mean values of the original degraded image with stripe and blur artifacts, where the vertical axis represents the mean intensity per column, and the horizontal axis corresponds to the column index of the image. Due to the relatively high level of noise introduced during degradation, the curve exhibits pronounced fluctuations.

In Figure 14, the blue curve represents the clear reference image, while the red curve denotes the restored result. It can be observed that in Figure 14a–d, significant fluctuations occur near each peak of the gray-level variations. In Figure 14h, distinct local oscillations appear around the lowest peak and several subsequent peaks, indicating a lack of smoothness in the restored image, which in turn reflects incomplete removal of stripe noise. In contrast, both the SLDR+eNeRf method and the proposed method yield smoother column-mean curves that closely follow the reference, suggesting that our method achieves better restoration performance. This observation is also consistent with the visual comparisons presented in Figure 11.

Based on the qualitative evaluation above, it is evident that when the image contains a significant stripe noise component and the degradation is severe, the effectiveness of stripe noise removal greatly impacts the subsequent deblurring performance. When the stripe noise removal is inadequate, applying the same deblurring algorithm does not lead to substantial improvement in image quality. To further evaluate the effectiveness of the proposed method, quantitative assessments are conducted on images from different scenarios. Specifically, the test images are categorized into two types: structurally complex and structurally flat scenes. For each evaluation metric, the average values are calculated and visualized using line plots to illustrate performance trends across different settings. Due to the limitation on figure quantity and size, 1000 representative infrared images from different scenes were selected for evaluation. The proposed method was applied to each image, and the quantitative results were averaged and presented in tabular form for clear comparison. The detailed quantitative results for different scenes are summarized in Table 1 and Table 2. The tabulated results clearly demonstrate that the proposed method outperforms the competing approaches in terms of quality metrics across both complex and flat terrain scenes.

In addition, to evaluate whether the performance differences among the competing methods are statistically significant across multiple evaluation metrics, independent significance tests were conducted on the metric values of each test image. For PSNR and SSIM, which approximately meet the normality assumption, the paired t-test was employed to compute the corresponding p-values. For the no-reference NIQE metric, which does not satisfy the normality assumption, the Wilcoxon signed-rank test was adopted to obtain the p-values. The statistical results for the three categories of evaluation metrics, including the corresponding p-values and significance decisions, are summarized in

Table 3. Statistical significance analysis compared on reference dataset (complex scene). The ✓ indicates satisfaction, while the × represents non-satisfaction.

Method	SSIM		PSNR		NIQE
	p-Value	Significance	p-Value	Significance	p-Value	Significance
LRSID+AMRN	0.0022	✓	0.0036	✓	0.0025	✓
ADOM+AMRN	0.0445	✓	0.0017	✓	0.0125	✓
LRSID+LGP	0.0088	✓	0.0019	✓	0.0016	✓
ADOM+LGP	0.1213	×	0.0058	✓	0.0535	×
ADOM+SCGTV	0.0465	✓	0.0009	✓	0.0149	✓
BSR_GLKM	0.0015	✓	0.0013	✓	0.0097	✓
RBDS	0.1086	×	0.0080	✓	0.0374	✓
De_GANv2	0.0421	✓	0.1373	×	0.0290	✓
SLDR eNeRf	0.0056	✓	0.0503	×	0.0084	✓

and

Table 4. Statistical significance analysis compared on reference dataset (flat scene). The ✓ indicates satisfaction, while the × represents non-satisfaction.

Method	SSIM		PSNR		NIQE
	p-Value	Significance	p-Value	Significance	p-Value	Significance
LRSID+AMRN	0.0059	✓	0.0030	✓	0.0047	✓
ADOM+AMRN	0.0394	✓	0.0035	✓	0.0193	✓
LRSID+LGP	0.0114	✓	0.0044	✓	0.0031	✓
ADOM+LGP	0.0560	×	0.0090	✓	0.0369	✓
ADOM+SCGTV	0.0392	✓	0.0031	✓	0.0229	✓
BSR_GLKM	0.0034	✓	0.0030	✓	0.0169	✓
RBDS	0.0491	✓	0.0103	✓	0.0305	✓
De_GANv2	0.0352	✓	0.1422	×	0.0369	✓
SLDR eNeRf	0.0078	✓	0.0460	✓	0.0130	✓

. As observed, our method achieves statistically significant improvements (p < 0.05) over most competing approaches. These results further demonstrate the effectiveness and robustness of the proposed algorithm.

3.3. No-Reference Image Data Experiments

In this section, we validate our method using in-orbit real TIS image data from the SDGSAT-1 satellite. The thermal infrared imager aboard SDGSAT-1 covers a swath width of 300 km, with a total of 286,538 scenes of shareable TIS data, with detection spectral bands of 8–10.5 $\mathsf{\mu }\mathrm{m}$, 10.3–11.3 $\mathsf{\mu }\mathrm{m}$ and 11.5–12.5 $\mathsf{\mu }\mathrm{m}$, and a spatial resolution of 30 m per pixel. Due to the large size of single remote sensing images, we crop the selected images into 800 × 800 pixel patches for experimental validation. Furthermore, the images processed by our method are locally enlarged to facilitate clearer observation of the restoration effects.

For real remote sensing images, due to their practical application requirements, stripe noise is generally less severe than that in simulated image data. A more notable difference lies in the higher imaging altitude, resulting in more complex scenes captured. As shown in Figure 15, we selected six images acquired by the SDGSAT-1 satellite at different times and locations. To quantitatively evaluate the restoration results on these real remote sensing images, we employ three no-reference image quality assessment metrics: Mean Relative Deviation (MRD), Image Contrast Value (ICV), and Natural Image Quality Evaluator (NIQE). Among these, a higher ICV indicates better restoration performance, whereas lower values of MRD and NIQE correspond to superior restoration quality. Based on the above evaluation criteria, we have bolded the highest ICV values and the lowest MRD and NIQE values in

Table 5. Average quality evaluation results on no-reference dataset (complex scene).

Method	NIQE/dB	ICV	MRD
LRSID+AMRN	6.3070	3.5237	0.0170
ADOM+AMRN	10.2284	3.3305	0.0128
LRSID+LGP	6.6622	3.6891	0.0189
ADOM+LGP	10.8664	3.4594	0.0145
ADOM+SCGTV	6.6598	3.3333	0.0143
BSR_GLKM	6.0957	3.4956	0.0124
RBDS	11.2188	3.4822	0.0147
De_GANv2	10.5114	3.4140	0.0778
SLDR_eNeRf	11.7117	3.3548	0.0139
Ours	6.0415	3.5124	0.0113

and

Table 6. Average quality evaluation results on no-reference dataset (flat scene).

Method	NIQE/dB	ICV	MRD
LRSID+AMRN	5.5713	46.3902	0.0722
ADOM+AMRN	6.8225	52.0792	0.0413
LRSID+LGP	6.1223	45.2617	0.0803
ADOM+LGP	7.5639	52.9108	0.0366
ADOM+SCGTV	6.5307	51.1732	0.0435
BSR_GLKM	5.8576	55.9826	0.0371
RBDS	8.6402	53.5716	0.0348
De_GANv2	8.4083	56.1115	0.0263
SLDR_eNeRf	8.8935	51.2671	0.0441
Ours	5.0817	59.4637	0.0173

to provide a clearer comparison and analysis of both the individual and comprehensive restoration performance of each method.

Figure 16 presents the restoration results of six real images from Figure 15 processed by different methods. Here, the regions of interest are further enlarged with yellow bounding boxes to facilitate a more intuitive comparison. From Figure 16a,c, it can be observed that LRSID leaves some residual stripes. These residual stripes, overlapping with ground scene details, cause subsequent deblurring steps to smooth out important ground information, resulting in an overly smoothed appearance. In contrast, Figure 16e,f show that SCGTV-based deblurring methods tend to excessively sharpen image details, leading to pronounced contrast in regions with large grayscale differences. After processing with the method shown in Figure 16d, the overall image grayscale level is slightly reduced, and an amplification of the wave patterns in the sea region is observed, which indirectly intensifies the image noise. From Figure 16b, although the stripe noise removal is effective, excessive processing of flat terrain areas results in significant noise extending along the geological features. The methods depicted in Figure 16g,h,i demonstrate relatively better restoration performance compared to other approaches. However, overall, the method proposed in this paper exhibits superior advantages and achieves better performance for these types of terrain images.

Next, we conduct a statistical analysis of the quantitative evaluation metrics for all methods applied to real remote sensing images. Due to the limitation on figure quantity and size, 1000 representative infrared images from different scenes were selected for evaluation. The proposed method was applied to each image, and the quantitative results were averaged and presented in tabular form for clear comparison. The results are presented in both tabular format (see Table 5 and Table 6). It can be observed from the tables that, for no-reference remote sensing datasets, the proposed method consistently demonstrates superior performance when comprehensively compared across evaluation metrics in both complex terrain and flat terrain scenarios.

In addition, to determine whether the performance differences among the compared methods are statistically significant across multiple evaluation metrics, we performed independent significance tests on the metric values of each test image. For metrics such as NIQE, ICV, and MRD, which do not satisfy the normality assumption or have unknown distributions, the Wilcoxon signed-rank test was applied to compute the p-values. The significance test results are reported in

Table 7. Statistical significance analysis compared on no-reference dataset (complex scene). The ✓ indicates satisfaction, while the × represents non-satisfaction.

Method	NIQE		ICV		MRD
	p-Value	Significance	p-Value	Significance	p-Value	Significance
LRSID+AMRN	0.0070	✓	0.0049	✓	0.0068	✓
ADOM+AMRN	0.0375	✓	0.0054	✓	0.0179	✓
LRSID+LGP	0.0145	✓	0.0559	×	0.0050	✓
ADOM+LGP	0.0552	×	0.0111	✓	0.0360	✓
ADOM+SCGTV	0.0383	✓	0.0050	✓	0.0222	✓
BSR_GLKM	0.0055	✓	0.0048	✓	0.0193	✓
RBDS	0.0482	✓	0.1125	×	0.0289	✓
De_GANv2	0.0331	✓	0.0447	✓	0.0558	×
SLDR eNeRf	0.0085	✓	0.0461	✓	0.0152	✓

and

Table 8. Statistical significance analysis compared on no-reference dataset (flat scene). The ✓ indicates satisfaction, while the × represents non-satisfaction.

Method	NIQE		ICV		MRD
	p-Value	Significance	p-Value	Significance	p-Value	Significance
LRSID+AMRN	0.0083	✓	0.0038	✓	0.0110	✓
ADOM+AMRN	0.0241	✓	0.0094	✓	0.0242	✓
LRSID+LGP	0.0202	✓	0.0431	✓	0.0099	✓
ADOM+LGP	0.0383	✓	0.0161	✓	0.0556	×
ADOM+SCGTV	0.0483	✓	0.0089	✓	0.0293	✓
BSR_GLKM	0.0115	✓	0.0087	✓	0.0258	✓
RBDS	0.0600	×	0.0361	✓	0.0372	✓
De_GANv2	0.0362	✓	0.0399	✓	0.0490	✓
SLDR eNeRf	0.0031	✓	0.0575	×	0.0210	✓

. As shown, our proposed method achieves statistically significant improvements over most competing approaches, further demonstrating its effectiveness and robustness.

The average runtime of the compared methods across different scenarios is summarized below. When comparing runtime performance, ten images were selected for each size category, and the average processing time was computed for comparison. DestripeGAN+PGDN and SLDR-NeRf are deep learning-based methods whose initial training time is not included in the reported runtimes; only the inference time for processing the images is considered, which accounts for their apparent time efficiency. Among all the compared methods, ADOM+SCGTV is the slowest due to the large number of iterations required for convergence. Although RBDS has relatively high computational complexity, its integration of deep learning components allows for a reasonably efficient runtime. Among the compared traditional algorithms, the runtime of our proposed method is significantly improved and is the shortest among all traditional methods. However, when considering runtime alone, deep learning-based methods demonstrate superior time efficiency. Detailed runtime comparisons are presented in

Table 9. Average runtime comparison on different image sizes.

Method	800 × 800 (s)	2000 × 2000 (s)	3000 × 3000 (s)
LRSID+AMRN	55.7932	62.6545	69.3894
ADOM+AMRN	60.8223	68.2977	76.5368
LRSID+LGP	50.1841	59.6472	66.3824
ADOM+LGP	64.5053	75.9931	87.3647
ADOM+SCGTV	136.3371	141.4861	148.3385
BSR_GLKM	3.38	3.64	3.97
RBDS	12.5620	14.6875	15.8611
De_GANv2	2.13	2.52	3.04
SLDR_eNeRf	2.42	2.85	3.26
Ours	32.1888	35.7643	39.3865

; the shortest runtimes for different image sizes are highlighted in bold to facilitate a clearer comparison and analysis of the computational efficiency across different methods.

3.4. Ablation Experiment

In this section, to clearly demonstrate the effectiveness of the proposed method, we conducted ablation experiments on three datasets: Jilin-1, MODIS, and SDGSAT-1. Specifically, two images were selected from each dataset and were degraded with a certain level of noise and blur. The ablation study was performed by sequentially removing key components of our method, including the edge-preserving operator based on structure tensor in the destriping stage, the fidelity term aligned with the stripe orientation, and the ringing suppression term designed to mitigate the impact of noise inside the estimated blur kernel during the non-blind restoration process. The comparative results are summarized in

Table 10. Average value of the evaluation index results for the ablation experiment.

	Edge Preserving	Stripe Orthogonal Fidelity	Ringing Suppression	SSIM	PSNR (dB)	NIQE
A	✓	✓	✓	0.9065	34.0333	5.9771
B	✓	✓	×	0.8586	29.1583	6.7023
C	✓	×	✓	0.8887	33.4699	6.1419
D	×	✓	✓	0.8882	33.1115	6.1821

.

Based on both the quantitative metrics and visual comparisons, it can be observed from Figure 17a,b,e,f,i,j, that the ringing suppression term has a significant impact on the quality of image restoration, particularly in mitigating oversmoothing at image edges. And by comparing the magnified central regions of Figure 17a,d, it can be observed that the edges around the ground parking lot appear sharper in Figure 17a than in (d), indicating the effectiveness of the proposed edge-preserving strategy. In addition, a comparison between Figure 17e,g reveals that some residual noise remains in Figure 17g, suggesting that noise removal is not fully achieved in that case. Furthermore, as shown in the magnified regions marked by red boxes in Figure 17k,l, the clarity of the riverbanks and surrounding rocks is noticeably inferior compared to that in Figure 17i.

Table 10 summarizes the quantitative evaluation results averaged over the 200 images used in the ablation experiment, demonstrating clear improvements in SSIM, PSNR, and NIQE. These results further substantiate the effectiveness and robustness of the proposed approach.

To further verify the robustness of the proposed algorithm under various imaging degradation conditions, we constructed multiple test cases with different blur levels (variances of 2, 4, 6, and 9) and varying stripe-noise intensities, and processed all samples using identical parameter settings. As shown in Figure 18 and

Table 11. Comparison of processing results under different imaging degradation conditions.

Metric	Variance 2 Noise [−40, 40]	Variance 4 Noise [−60, 60]	Variance 6 Noise [−60, 60]	Variance 9 Noise [−80, 80]
SSIM	0.9491	0.8623	0.7314	0.6003
PSNR (dB)	32.1084	28.0056	25.2211	20.7588

, the degree of image degradation increases as the noise variance becomes larger. Nevertheless, the proposed method consistently suppresses noise while preserving the principal structural information. When the noise variance is 2 (noise range: [−40, 40]), the reconstructed image exhibits high visual quality, with SSIM and PSNR reaching 0.9491 and 32.11 dB, indicating that the method can almost fully recover fine details under low-noise conditions. As the noise variance increases to 4 and 6 (noise range: [−60, 60]), the reconstruction quality decreases moderately, with SSIM dropping to 0.8623 and 0.7314 and PSNR decreasing to 28.01 dB and 25.22 dB, respectively; however, the main structural information remains well preserved. When the variance further increases to 9 (noise range: [−80, 80]), the image becomes severely degraded, yet the algorithm still maintains noticeable restoration capability, achieving an SSIM of 0.6003 and a PSNR of 20.76 dB. These results collectively demonstrate that the proposed method retains strong robustness even under severe noise conditions.

4. Discussion

Based on the experimental results, the proposed three-stage joint destriping and deblurring restoration framework demonstrates stable and superior recovery performance over comparative methods under various degradation scenarios. The analysis indicates that the strong directionality of stripe noise in the gradient domain is one of the key factors leading to the instability of blur kernel estimation in traditional blind deblurring methods. Introducing a stripe-specific suppression mechanism prior to kernel estimation effectively mitigates its interference, thereby improving the accuracy of the kernel morphology and energy distribution. Meanwhile, the adaptive regularization strategy constructed based on the structure tensor shows a clear advantage in distinguishing between genuine edge structures and directional stripe noise. This enables the stripe suppression process to better preserve ground object boundaries and fine details, providing reliable structural priors for subsequent restoration.

In the non-blind restoration stage, the proposed WCOB ringing suppression model achieves an effective balance between detail recovery and stability through a signal-to-noise ratio (SNR)-based adaptive weighting mechanism. Compared with conventional Wiener filtering, the proposed model significantly reduces ringing artifacts near strong edges while avoiding detail loss caused by over-smoothing. It should be noted that although the proposed method achieves consistent performance improvements on both simulated data and real satellite-based infrared remote sensing images, its computational complexity remains relatively high. Moreover, the current model assumes that the stripe direction is known and relatively fixed; thus, its adaptability to stripes with varying directions or non-periodic noise requires further enhancement. Future work will focus on algorithm acceleration, model lightweighting, and integration with deep learning methods to improve the practicality and robustness of the approach in real-world remote sensing applications.

5. Conclusions

In this work, we proposed a three-stage non-blind image restoration framework tailored for infrared remote sensing imagery, which integrates stripe noise removal and blur kernel estimation in a unified manner. The first stage leverages wavelet decomposition and a structure tensor-based adaptive edge-preserving operator to precisely extract stripe noise while preserving fine structural details. Next, a regularized model incorporating vertical gradient fidelity and a Laplacian operator is constructed to suppress the impact of stripe noise on kernel estimation, thereby improving the accuracy of the estimated blur kernel. Finally, we developed a WCOB comprehensive restoration model to mitigate ringing artifacts and pseudo-edges. This model achieves high-quality deblurring. Extensive experiments on both simulated and real data from Jilin-1 and SDGSAT-1 TIS satellites validate the effectiveness of the proposed approach. The method demonstrates superior performance in stripe removal and image restoration across diverse scenarios, achieving notable improvements in SSIM, PSNR, and NIQE metrics. These results highlight the method’s strong generalization ability and practical applicability, making it a valuable contribution to the field of infrared remote sensing image processing.

Although the proposed method achieves promising results in both destriping and deblurring tasks, it still depends on several regularization parameters. Despite extensive empirical tuning, some parameters may require manual adjustment under specific imaging conditions to ensure optimal performance, which limits the overall generalizability of the framework. In addition, the current method has been primarily evaluated on infrared remote sensing imagery, and its effectiveness in extremely low-light environments or under highly dynamic illumination conditions has yet to be fully assessed. Given the increasing complexity and diversity of remote sensing scenarios, joint deblurring under stripe noise remains a highly valuable research direction. In future work, we plan to incorporate deep neural networks into the framework to further improve its robustness and adaptability in complex imaging environments. Moreover, efforts will be directed toward lightweight model optimization to meet the computational constraints of onboard satellite processors, ultimately enabling real-time, edge-oriented image restoration for spaceborne remote sensing platforms.