Zhiyuan Zha

Analyzing the group sparsity based on the rank minimization methods

Sparse coding has achieved a great success in various image processing studies. However, there is not any benchmark to measure the sparsity of image patch/group because sparse discriminant conditions cannot keep unchanged. This paper analyzes the sparsity of group based on the strategy of the rank minimization. Firstly, an adaptive dictionary for each group is designed. Then, we prove that group-based sparse coding is equivalent to the rank minimization problem, and thus the sparse coefficients of each group are measured by estimating the singular values of each group. Based on that measurement, the weighted Schatten p-norm minimization (WSNM) has been found to be the closest solution to the real singular values of each group. Thus, WSNM can be equivalently transformed into a non-convex ℓp-norm minimization problem in group-based sparse coding. Experimental results on two applications: image in painting and image compressive sensing (CS) recovery show that the proposed scheme outperforms many state-of-the-art methods.

Compressed sensing image reconstruction via adaptive sparse nonlocal regularization

Compressed sensing (CS) has been successfully utilized by many computer vision applications. However,the task of signal reconstruction is still challenging, especially when we only have the CS measurements of an image (CS image reconstruction). Compared with the task of traditional image restoration (e.g., image denosing, debluring and inpainting, etc.), CS image reconstruction has partly structure or local features. It is difficult to build a dictionary for CS image reconstruction from itself. Few studies have shown promising reconstruction performance since most of the existing methods employed a fixed set of bases (e.g., wavelets, DCT, and gradient spaces) as the dictionary, which lack the adaptivity to fit image local structures. In this paper, we propose an adaptive sparse nonlocal regularization (ASNR) approach for CS image reconstruction. In ASNR, an effective self-adaptive learning dictionary is used to greatly reduce artifacts and the loss of fine details. The dictionary is compact and learned from the reconstructed image itself rather than natural image dataset. Furthermore, the image sparse nonlocal (or nonlocal self-similarity) priors are integrated into the regularization term, thus ASNR can effectively enhance the quality of the CS image reconstruction. To improve the computational efficiency of the ASNR, the split Bregman iteration based technique is also developed, which can exhibit better convergence performance than iterative shrinkage/thresholding method. Extensive experimental results demonstrate that the proposed ASNR method can effectively reconstruct fine structures and suppress visual artifacts, outperforming state-of-the-art performance in terms of both the PSNR and visual measurements.

Image denoising via group sparsity residual constraint

Group sparsity has shown great potential in various low-level vision tasks (e.g, image denoising, deblurring and inpainting). In this paper, we propose a new prior model for image denoising via group sparsity residual constraint (GSRC). To enhance the performance of group sparse-based image denoising, the concept of group sparsity residual is proposed, and thus, the problem of image denoising is translated into one that reduces the group sparsity residual. To reduce the residual, we first obtain some good estimation of the group sparse coefficients of the original image by the first-pass estimation of noisy image, and then centralize the group sparse coefficients of noisy image to the estimation. Experimental results have demonstrated that the proposed method not only outperforms many state-of-the-art denoising methods such as BM3D and WNNM, but results in a faster speed.

Group Sparsity Residual Constraint for Image Denoising with External Nonlocal Self-Similarity Prior

Abstract Nonlocal image representation has been successfully used in many image-related inverse problems including denoising, deblurring and deblocking. However, most existing methods only consider the nonlocal self-similarity (NSS) prior of degraded observation image, and few methods use the NSS prior from natural images. In this paper we propose a novel method for image denoising via group sparsity residual constraint with external NSS prior (GSRC-ENSS). Different from the previous NSS prior-based denoising methods, two kinds of NSS prior (e.g., NSS priors of noisy image and natural images) are used for image denoising. In particular, to enhance the performance of image denoising, the group sparsity residual is proposed, and thus the problem of image denoising is translated into reducing the group sparsity residual. Because the groups contain a large amount of NSS information of natural images, to reduce the group sparsity residual, we obtain a good estimation of the group sparse coefficients of the original image by the external NSS prior based on Gaussian Mixture Model (GMM) learning, and the group sparse coefficients of noisy image are used to approximate the estimation. To combine these two NSS priors better, an effective iterative shrinkage algorithm is developed to solve the proposed GSRC-ENSS model. Experimental results demonstrate that the proposed GSRC-ENSS not only outperforms several state-of-the-art methods, but also delivers the best qualitative denoising results with finer details and less ringing artifacts.

Group-based sparse representation for image compressive sensing reconstruction with non-convex regularization

Patch-based sparse representation modeling has shown great potential in image compressive sensing (CS) reconstruction. However, this model usually suffers from some limits, such as dictionary learning with great computational complexity, neglecting the relationship among similar patches. In this paper, a group-based sparse representation method with non-convex regularization (GSR-NCR) for image CS reconstruction is proposed. In GSR-NCR, the local sparsity and nonlocal self-similarity of images is simultaneously considered in a unified framework. Different from the previous methods based on sparsity-promoting convex regularization, we extend the non-convex weighted Lp (0 < p < 1) penalty function on group sparse coefficients of the data matrix, rather than conventional L1-based regularization. To reduce the computational complexity, instead of learning the dictionary with a high computational complexity from natural images, we learn the principle component analysis (PCA) based dictionary for each group. Moreover, to make the proposed scheme tractable and robust, we have developed an efficient iterative shrinkage/thresholding algorithm to solve the non-convex optimization problem. Experimental results demonstrate that the proposed method outperforms many state-of-the-art techniques for image CS reconstruction.

Non-convex weighted ℓ p nuclear norm based ADMM framework for image restoration

Abstract Inspired by the fact that the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used in various image processing studies. Nonetheless, nuclear norm based convex surrogate of the rank function usually over-shrinks the rank components since it treats different components equally, and thus may produce a result far from the optimum. To alleviate the aforementioned limitations of the nuclear norm, in this paper we propose a new method for image restoration via the non-convex weighted lp nuclear norm minimization (NCW-NNM), which is able to accurately impose the image structural sparsity and self-similarity simultaneously. To make the proposed model tractable and robust, the alternating direction method of multiplier (ADMM) framework is adopted to solve the associated non-convex minimization problem. Experimental results on various image restoration problems, including image deblurring, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed method outperforms many current state-of-the-art methods.