Image Restoration Using Joint Statistical Modeling in Space-Transform Domain

This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First, from the perspective of image statistics, a joint statistical modeling (JSM) in an adaptive hybrid space-transform domain is established, which offers a powerful mechanism of combining local smoothness and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Second, a new form of minimization functional for solving image inverse problem is formulated using JSM under regularization-based framework. Finally, in order to make JSM tractable and robust, a new Split-Bregman based algorithm is developed to efficiently solve the above severely underdetermined inverse problem associated with theoretical proof of convergence. Extensive experiments on image inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions on Circuits System and Video Technology (TCSVT). High resolution pdf version and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM

Improved Total Variation based Image Compressive Sensing Recovery by Nonlocal Regularization

Recently, total variation (TV) based minimization algorithms have achieved great success in compressive sensing (CS) recovery for natural images due to its virtue of preserving edges. However, the use of TV is not able to recover the fine details and textures, and often suffers from undesirable staircase artifact. To reduce these effects, this letter presents an improved TV based image CS recovery algorithm by introducing a new nonlocal regularization constraint into CS optimization problem. The nonlocal regularization is built on the well known nonlocal means (NLM) filtering and takes advantage of self-similarity in images, which helps to suppress the staircase effect and restore the fine details. Furthermore, an efficient augmented Lagrangian based algorithm is developed to solve the above combined TV and nonlocal regularization constrained problem. Experimental results demonstrate that the proposed algorithm achieves significant performance improvements over the state-of-the-art TV based algorithm in both PSNR and visual perception.Comment: 4 Pages, 1 figures, 3 tables, to be published at IEEE Int. Symposium of Circuits and Systems (ISCAS) 201