As a fundamental task in image processing, blind image restoration (BIR) faces significant challenges due to the unknown nature of the degradation process. While transformer-based methods have shown promise in various applications, they encounter difficulties in BIR. One key challenge is that the complexity of degradation easily leads to incorporate irrelevant information into their attention mechanisms, thereby hindering restoration performance. To address this challenge, sparsification strategies have been commonly adopted. However, existing sparse transformer-based methods typically determine sparse members through fixed patterns such as constant thresholds or predefined sources, making their sparsification strategies too rigid. To tackle this issue, we propose WSformer, a Wavelet-based Sparse transformer tailored for BIR, which offers three key advantages. First, we design a Sparse Reciprocal Multi-head Self-Attention (SR-MSA) mechanism in the attention layer. This mechanism employs sparse and reciprocal strategies to adaptively select reliable information, while operating across channels to reduce computational complexity. Second, recognizing that feed-forward networks in existing transformer blocks fail to effectively leverage global information, we develop a Recalibrated Feed-Forward Network (RFFN). It fully exploits the fusion of local and global information, enhancing the robustness of feature learning. Finally, to mitigate the increased computational burden introduced by these innovations, we equip WSformer with wavelet transform. Combined with a U-shaped architecture, it enables WSformer to achieve an optimal balance between performance and inference time. Extensive experiments on multiple BIR tasks validate WSformer's effectiveness in both quantitative metrics and visual quality. The code is available at https://github.com/CanZhang01/WSformer.

Non-local block (NLB) is a breakthrough technology in computer vision. It greatly boosts the capability of deep convolutional neural networks (CNNs) to capture long-range dependencies. As the critical component of NLB, non-local operation can be considered a network-based implementation of the well-known non-local means filter (NLM). Drawing on the solid theoretical foundation of NLM, we provide an innovative interpretation of the non-local operation. Specifically, it is formulated as an optimization problem regularized by Shannon entropy with a fixed parameter. Building on this insight, we further introduce an adaptive regularization strategy to enhance NLB and get a novel non-local block named ARNLB. Preliminary experiments on semantic segmentation demonstrate its effectiveness.

Plug-and-play (PnP) is a powerful framework that applies off-the-shelf denoisers to regularize imaging inverse problems in an iterative style. Remarkably, in several restoration applications, this kind of regularization exhibits promising behaviors. Among the algorithms derived from the framework, the ISTA-based (PnP-ISTA) has attracted much attentions due to the effectiveness and simple update rule in iterations. And its convergence analysis has become a fundamental topic. Most recently, the theoretical convergence of PnP-ISTA with kernel denoisers has been established, where the kernel is generic (relaxing the reliance on special properties) and thus beneficial for wider applications. In there, the convergence proof focuses on fixed kernels. Note that, the denoisers with adaptive kernels usually achieve more powerful performance than those with fixed ones. Inspired by the preliminary observation, we extend the fixed kernels to adaptive ones for the denoisers in PnP-ISTA. Under a mild assumption, we prove the convergence theoretically. Meanwhile, for inpainting, an important scenario, we broaden the interval of the step size from 01to02, which still guarantees the convergence. Experimental results agree with our theoretical conclusions.

Due to its local property, guided image filter (GIF) generally suffers from halo artifacts near edges. To make up for the deficiency, a weighted guided image filter (WGIF) was proposed recently by incorporating an edge-aware weighting into the filtering process. It takes the advantages of local and global operations, and achieves better performance in edge-preserving. However, edge direction, a vital property of the guidance image, is not considered fully in these guided filters. In order to overcome the drawback, we propose a novel version of GIF, which can leverage the edge direction more sufficiently. In particular, we utilize the steering kernel to adaptively learn the direction and incorporate the learning results into the filtering process to improve the filter's behavior. Theoretical analysis shows that the proposed method can get more powerful performance with preserving edges and reducing halo artifacts effectively. Similar conclusions are also reached through the thorough experiments including edge-aware smoothing, detail enhancement, denoising and dehazing.

A nonlocal operator model for morphological image processing is proposed in this paper. Compared with the previous nonlocal morphological operators, the derivations of the proposed model are easier to inherit useful properties and physical interpretations from the traditional morphology. Two important properties of the model have been clarified in theory. And for instances, based on the model, two basic morphological operators (i.e., erosion and dilatation) are developed with convincing experimental results. In addition, the generality and usability of the model are also discussed.

Non-Local Euclidean Medians (NLEM) has recently been proposed and shows more effective than Non-Local Means (NLM) in removing heavy noise. In this letter, we find the inconsistency between the two dissimilarity measures in NLEM can affect its robustness, thus develop an improved version (INLEM) to compensate such an inconsistency. Further, we provide a concise convergence proof for the iterative algorithm used in both NLEM and INLEM. Finally, our experiments on synthetic and natural images show that INLEM achieves encouraging results.