Image restoration using joint statistical modeling in a 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-fold. 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 the image inverse problem is formulated using JSM under a 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.