Image Restoration Using Joint Statistical Modeling in Space-Transform Domain

TL;DR

This paper introduces a joint statistical modeling approach in a space-transform domain for high-quality image restoration, effectively combining local and nonlocal image features for improved results.

Contribution

It proposes a novel joint statistical model in an adaptive hybrid space-transform domain and a new algorithm with convergence proof for robust image restoration.

Findings

Effective in image inpainting, deblurring, and noise removal

Outperforms existing methods in quality and robustness

Converges reliably with the proposed Split-Bregman algorithm

Abstract

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.