Sparse coding has achieved a great success in various image processing tasks. However, a benchmark to measure the sparsity of image patch/group is missing since sparse coding is essentially an NP-hard problem. This work attempts to fill the gap from the perspective of rank minimization. We firstly design an adaptive dictionary to bridge the gap between group-based sparse coding (GSC) and rank minimization. Then, we show that under the designed dictionary, GSC and the rank minimization problems are equivalent, and therefore the sparse coefficients of each patch group can be measured by estimating the singular values of each patch group. We thus earn a benchmark to measure the sparsity of each patch group because the singular values of the original image patch groups can be easily computed by the singular value decomposition (SVD). This benchmark can be used to evaluate performance of any kind of norm minimization methods in sparse coding through analyzing their corresponding rank minimization counterparts. Towards this end, we exploit four well-known rank minimization methods to study the sparsity of each patch group and the weighted Schatten p-norm minimization (WSNM) is found to be the closest one to the real singular values of each patch group. Inspired by the aforementioned equivalence regime of rank minimization and GSC, WSNM can be translated into a non-convex weighted ℓp-norm minimization problem in GSC. By using the earned benchmark in sparse coding, the weighted ℓp-norm minimization is expected to obtain better performance than the three other norm minimization methods, i.e., ℓ1-norm, ℓp-norm and weighted ℓ1-norm. To verify the feasibility of the proposed benchmark, we compare the weighted ℓp-norm minimization against the three aforementioned norm minimization methods in sparse coding. Experimental results on image restoration applications, namely image inpainting and image compressive sensing recovery, demonstrate that the proposed scheme is feasible and outperforms many state-of-the-art methods.

In this paper, we propose a novel approach for the rank minimization problem, termed rank residual constraint (RRC). Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the weighted nuclear norm minimization (WNNM), which estimate the underlying low-rank matrix directly from the corrupted observation, we progressively approximate (approach) the underlying low-rank matrix via minimizing the rank residual. Through integrating the image nonlocal self-similarity (NSS) prior with the proposed RRC model, we apply it to image restoration tasks, including image denoising and image compression artifacts reduction. Toward this end, we first obtain a good reference of the original image groups by using the image NSS prior, and then the rank residual of the image groups between this reference and the degraded image is minimized to achieve a better estimate to the desired image. In this manner, both the reference and the estimated image in each iteration are improved gradually and jointly. Based on the group-based sparse representation model, we further provide a theoretical analysis on the feasibility of the proposed RRC model. Experimental results demonstrate that the proposed RRC model outperforms many state-of-the-art schemes in both the objective and perceptual qualities.

Sparse representation has achieved great success in various image processing and computer vision tasks. For image processing, typical patch-based sparse representation (PSR) models usually tend to generate undesirable visual artifacts, while group-based sparse representation (GSR) models lean to produce over-smooth effects. In this paper, we propose a new sparse representation model, termed joint patch-group based sparse representation (JPG-SR). Compared with existing sparse representation models, the proposed JPG-SR provides an effective mechanism to integrate the local sparsity and nonlocal self-similarity of images. We then apply the proposed JPG-SR to image restoration tasks, including image inpainting and image deblocking. An iterative algorithm based on the alternating direction method of multipliers (ADMM) framework is developed to solve the proposed JPG-SR based image restoration problems. Experimental results demonstrate that the proposed JPG-SR is effective and outperforms many state-of-the-art methods in both objective and perceptual quality.

Contrastive learning has been successfully leveraged to learn action representations for addressing the problem of semisupervised skeleton-based action recognition. However, most contrastive learning-based methods only contrast global features mixing spatiotemporal information, which confuses the spatial-and temporal-specific information reflecting different semantic at the frame level and joint level. Thus, we propose a novel spatiotemporal decouple-and-squeeze contrastive learning (SDS-CL) framework to comprehensively learn more abundant representations of skeleton-based actions by jointly contrasting spatial-squeezing features, temporal-squeezing features, and global features. In SDS-CL, we design a new spatiotemporal-decoupling intra–inter attention (SIIA) mechanism to obtain the spatiotemporal-decoupling attentive features for capturing spatiotemporal specific information by calculating spatial-and temporal-decoupling intra-attention maps among joint/motion features, as well as spatial-and temporal-decoupling inter-attention maps between joint and motion features. Moreover, we present a new spatial-squeezing temporal-contrasting loss (STL), a new temporal-squeezing spatial-contrasting loss (TSL), and the global-contrasting loss (GL) to contrast the spatial-squeezing joint and motion features at the frame level, temporal-squeezing joint and motion features at the joint level, as well as global joint and motion features at the skeleton level. Extensive experimental results on four public datasets show that the proposed SDS-CL achieves performance gains compared with other competitive methods.

This paper describes a study aimed at comparing the real image sensor noise distribution to the models of noise often assumed in image denoising designs. A quantile analysis in pixel, wavelet transform, and variance stabilization domains reveal that the tails of Poisson, signal-dependent Gaussian, and Poisson-Gaussian models are too short to capture real sensor noise behavior. A new Poisson mixture noise model is proposed to correct the mismatch of tail behavior. Based on the fact that noise model mismatch results in image denoising that undersmoothes real sensor data, we propose a mixture of Poisson denoising method to remove the denoising artifacts without affecting image details, such as edge and textures. Experiments with real sensor data verify that denoising for real image sensor data is indeed improved by this new technique.

The non-local-based model for hyperspectral image (HSI) denoising first uses non-local self-similarity (NSS) prior to group similar full-band patches into three-dimensional non-local full-band groups (tensors) using a block matching (BM) operation, and then a low-rank (LR) penalty is typically applied to each non-local full-band group to reduce noise. While non-local-based methods have shown promising performance in HSI denoising, most existing methods have only considered the LR property of the non-local full-band group while ignoring the strong correlation between sparse coefficients. Moreover, such methods often result in unsatisfactory visual artifacts due to the noise sensitivity of BM operations, while requiring expensive computations. To address these limitations, this paper proposes a novel non-local structured sparsity regularization (NLSSR) approach for HSI denoising. First, to mitigate the noise sensitivity of the BM operation, we propose a graph-based domain distance scheme to index similar full-band patches to form the non-local full-band group. Second, we design an adaptive unidirectional low-rank (LR) dictionary with low complexity that takes into account the differences in intrinsic structure correlation among different modes of the non-local full-band tensor. Third, we utilize a global spectral LR prior to reduce spectral redundancy. Fourth, we develop a generalized soft-thresholding (GST) algorithm based on the alternating minimization framework to solve the NLSSR-based HSI denoising problem. We perform extensive experiments on both simulated and real data to show that the proposed NLSSR algorithm outperforms many popular or state-of-the-art HSI denoising methods in both quantitative and visual evaluations.