A Hybrid Structural Sparsification Error Model for Image Restoration

DEs-Inspired Accelerated Unfolded Linearized ADMM Networks for Inverse Problems

Many research works have shown that the traditional alternating direction multiplier methods (ADMMs) can be better understood by continuous-time differential equations (DEs). On the other hand, many unfolded algorithms directly inherit the traditional iterations to build deep networks. Although they achieve superior practical performance and a faster convergence rate than traditional counterparts, there is a lack of clear insight into unfolded network structures. Thus, we attempt to explore the unfolded linearized ADMM (LADMM) from the perspective of DEs, and design more efficient unfolded networks. First, by proposing an unfolded Euler LADMM scheme and inspired by the trapezoid discretization, we design a new more accurate Trapezoid LADMM scheme. For the convenience of implementation, we provide its explicit version via a prediction-correction strategy. Then, to expand the representation space of unfolded networks, we design an accelerated variant of our Euler LADMM scheme, which can be interpreted as second-order DEs with stronger representation capabilities. To fully explore this representation space, we designed an accelerated Trapezoid LADMM scheme. To the best of our knowledge, this is the first work to explore a comprehensive connection with theoretical guarantees between unfolded ADMMs and first- (second-) order DEs. Finally, we instantiate our schemes as (A-)ELADMM and (A-)TLADMM with the proximal operators, and (A-)ELADMM-Net and (A-)TLADMM-Net with convolutional neural networks (CNNs). Extensive inverse problem experiments show that our Trapezoid LADMM schemes perform better than well-known methods.

Sparse representation for restoring images by exploiting topological structure of graph of patches

Image restoration poses a significant challenge, aiming to accurately recover damaged images by delving into their inherent characteristics. Various models and algorithms have been explored by researchers to address different types of image distortions, including sparse representation, grouped sparse representation, and low‐rank self‐representation. The grouped sparse representation algorithm leverages the prior knowledge of non‐local self‐similarity and imposes sparsity constraints to maintain texture information within images. To further exploit the intrinsic properties of images, this study proposes a novel low‐rank representation‐guided grouped sparse representation image restoration algorithm. This algorithm integrates self‐representation models and trace optimization techniques to effectively preserve the original image structure, thereby enhancing image restoration performance while retaining the original texture and structural information. The proposed method was evaluated on image denoising and deblocking tasks across several datasets, demonstrating promising results.

Image restoration with group sparse representation and low‐rank group residual learning

Image restoration, as a fundamental research topic of image processing, is to reconstruct the original image from degraded signal using the prior knowledge of image. Group sparse representation (GSR) is powerful for image restoration; it however often leads to undesirable sparse solutions in practice. In order to improve the quality of image restoration based on GSR, the sparsity residual model expects the representation learned from degraded images to be as close as possible to the true representation. In this article, a group residual learning based on low‐rank self‐representation is proposed to automatically estimate the true group sparse representation. It makes full use of the relation among patches and explores the subgroup structures within the same group, which makes the sparse residual model have better interpretation furthermore, results in high‐quality restored images. Extensive experimental results on two typical image restoration tasks (image denoising and deblocking) demonstrate that the proposed algorithm outperforms many other popular or state‐of‐the‐art image restoration methods.

Sparse Representation-Based Multi-Focus Image Fusion Method via Local Energy in Shearlet Domain

Multi-focus image fusion plays an important role in the application of computer vision. In the process of image fusion, there may be blurring and information loss, so it is our goal to obtain high-definition and information-rich fusion images. In this paper, a novel multi-focus image fusion method via local energy and sparse representation in the shearlet domain is proposed. The source images are decomposed into low- and high-frequency sub-bands according to the shearlet transform. The low-frequency sub-bands are fused by sparse representation, and the high-frequency sub-bands are fused by local energy. The inverse shearlet transform is used to reconstruct the fused image. The Lytro dataset with 20 pairs of images is used to verify the proposed method, and 8 state-of-the-art fusion methods and 8 metrics are used for comparison. According to the experimental results, our method can generate good performance for multi-focus image fusion.

Multi-Color Channels Based Group Sparse Model for Image Restoration

The group sparse representation (GSR) model combines local sparsity and nonlocal similarity in image processing, and achieves excellent results. However, the traditional GSR model and all subsequent improved GSR models convert the RGB space of the image to YCbCr space, and only extract the Y (luminance) channel of YCbCr space to change the color image to a gray image for processing. As a result, the image processing process cannot be loyal to each color channel, so the repair effect is not ideal. A new group sparse representation model based on multi-color channels is proposed in this paper. The model processes R, G and B color channels simultaneously when processing color images rather than processing a single color channel and then combining the results of different channels. The proposed multi-color-channels-based GSR model is compared with state-of-the-art methods. The experimental contrast results show that the proposed model is an effective method and can obtain good results in terms of objective quantitative metrics and subjective visual effects.

Wavelet Frequency Separation Attention Network for Chest X-ray Image Super-Resolution

Medical imaging is widely used in medical diagnosis. The low-resolution image caused by high hardware cost and poor imaging technology leads to the loss of relevant features and even fine texture. Obtaining high-quality medical images plays an important role in disease diagnosis. A surge of deep learning approaches has recently demonstrated high-quality reconstruction for medical image super-resolution. In this work, we propose a light-weight wavelet frequency separation attention network for medical image super-resolution (WFSAN). WFSAN is designed with separated-path for wavelet sub-bands to predict the wavelet coefficients, considering that image data characteristics are different in the wavelet domain and spatial domain. In addition, different activation functions are selected to fit the coefficients. Inputs comprise approximate sub-bands and detail sub-bands of low-resolution wavelet coefficients. In the separated-path network, detail sub-bands, which have more sparsity, are trained to enhance high frequency information. An attention extension ghost block is designed to generate the features more efficiently. All results obtained from fusing layers are contracted to reconstruct the approximate and detail wavelet coefficients of the high-resolution image. In the end, the super-resolution results are generated by inverse wavelet transform. Experimental results show that WFSAN has competitive performance against state-of-the-art lightweight medical imaging methods in terms of quality and quantitative metrics.

Simultaneous Patch-Group Sparse Coding with Dual-Weighted ℓp Minimization for Image Restoration

Sparse coding (SC) models have been proven as powerful tools applied in image restoration tasks, such as patch sparse coding (PSC) and group sparse coding (GSC). However, these two kinds of SC models have their respective drawbacks. PSC tends to generate visually annoying blocking artifacts, while GSC models usually produce over-smooth effects. Moreover, conventional ℓ1 minimization-based convex regularization was usually employed as a standard scheme for estimating sparse signals, but it cannot achieve an accurate sparse solution under many realistic situations. In this paper, we propose a novel approach for image restoration via simultaneous patch-group sparse coding (SPG-SC) with dual-weighted ℓp minimization. Specifically, in contrast to existing SC-based methods, the proposed SPG-SC conducts the local sparsity and nonlocal sparse representation simultaneously. A dual-weighted ℓp minimization-based non-convex regularization is proposed to improve the sparse representation capability of the proposed SPG-SC. To make the optimization tractable, a non-convex generalized iteration shrinkage algorithm based on the alternating direction method of multipliers (ADMM) framework is developed to solve the proposed SPG-SC model. Extensive experimental results on two image restoration tasks, including image inpainting and image deblurring, demonstrate that the proposed SPG-SC outperforms many state-of-the-art algorithms in terms of both objective and perceptual quality.

Image Restoration via Reconciliation of Group Sparsity and Low-Rank Models

Image nonlocal self-similarity (NSS) property has been widely exploited via various sparsity models such as joint sparsity (JS) and group sparse coding (GSC). However, the existing NSS-based sparsity models are either too restrictive, e.g., JS enforces the sparse codes to share the same support, or too general, e.g., GSC imposes only plain sparsity on the group coefficients, which limit their effectiveness for modeling real images. In this paper, we propose a novel NSS-based sparsity model, namely, low-rank regularized group sparse coding (LR-GSC), to bridge the gap between the popular GSC and JS. The proposed LR-GSC model simultaneously exploits the sparsity and low-rankness of the dictionary-domain coefficients for each group of similar patches. An alternating minimization with an adaptive adjusted parameter strategy is developed to solve the proposed optimization problem for different image restoration tasks, including image denoising, image deblocking, image inpainting, and image compressive sensing. Extensive experimental results demonstrate that the proposed LR-GSC algorithm outperforms many popular or state-of-the-art methods in terms of objective and perceptual metrics.