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.

本文提出了一种新的高保真图像恢复策略，通过将自然图像的局部平滑性和非局部自相似性统一建模，采用联合统计建模和基于正则化的框架，设计出新形式的最小化目标函数，并用基于Split-Bregman的算法解决该问题，实现图片去噪、去模糊和修补，验证该算法的有效性。

利用空间变换联合统计建模进行图像恢复