Zha Zhiyuan, Yuan Xin, Wen Bihan, Zhou Jiantao, Zhu Ce
IEEE Trans Image Process. 2020 Sep 9;PP. doi: 10.1109/TIP.2020.3021291.
Group sparse representation (GSR) has made great strides in image restoration producing superior performance, realized through employing a powerful mechanism to integrate the local sparsity and nonlocal self-similarity of images. However, due to some form of degradation (e.g., noise, down-sampling or pixels missing), traditional GSR models may fail to faithfully estimate sparsity of each group in an image, thus resulting in a distorted reconstruction of the original image. This motivates us to design a simple yet effective model that aims to address the above mentioned problem. Specifically, we propose group sparsity residual constraint with nonlocal priors (GSRC-NLP) for image restoration. Through introducing the group sparsity residual constraint, the problem of image restoration is further defined and simplified through attempts at reducing the group sparsity residual. Towards this end, we first obtain a good estimation of the group sparse coefficient of each original image group by exploiting the image nonlocal self-similarity (NSS) prior along with self-supervised learning scheme, and then the group sparse coefficient of the corresponding degraded image group is enforced to approximate the estimation. To make the proposed scheme tractable and robust, two algorithms, i.e., iterative shrinkage/thresholding (IST) and alternating direction method of multipliers (ADMM), are employed to solve the proposed optimization problems for different image restoration tasks. Experimental results on image denoising, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed GSRC-NLP based image restoration algorithm is comparable to state-of-the-art denoising methods and outperforms several state-of-the-art image inpainting and image CS recovery methods in terms of both objective and perceptual quality metrics.
组稀疏表示（GSR）在图像恢复方面取得了巨大进展，通过采用强大的机制来整合图像的局部稀疏性和非局部自相似性，实现了卓越的性能。然而，由于某种形式的退化（例如噪声、下采样或像素缺失），传统的GSR模型可能无法准确估计图像中每个组的稀疏性，从而导致原始图像的重建失真。这促使我们设计一个简单而有效的模型来解决上述问题。具体而言，我们提出了用于图像恢复的具有非局部先验的组稀疏残差约束（GSRC-NLP）。通过引入组稀疏残差约束，图像恢复问题通过尝试减少组稀疏残差得到了进一步定义和简化。为此，我们首先利用图像非局部自相似性（NSS）先验以及自监督学习方案，对每个原始图像组的组稀疏系数进行良好估计，然后强制相应退化图像组的组稀疏系数近似该估计。为了使所提出的方案易于处理且稳健，采用了两种算法，即迭代收缩/阈值化（IST）和交替方向乘子法（ADMM），来解决针对不同图像恢复任务提出的优化问题。在图像去噪、图像修复和图像压缩感知（CS）恢复方面的实验结果表明，所提出的基于GSRC-NLP的图像恢复算法与当前最先进的去噪方法相当，并且在客观和感知质量指标方面均优于几种当前最先进的图像修复和图像CS恢复方法。
