# Image Restoration Using Joint Statistical Modeling in Space-Transform Domain

arXiv: https://arxiv.org/abs/1405.3173 · HTML: https://mlsanity.com/paper/1405.3173/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2014.

## Built on by (most cited first, 4 of 4)

- [Dynamic Attentive Graph Learning for Image Restoration](https://mlsanity.com/paper/2109.06620/) (2021)
- [COLA-Net: Collaborative Attention Network for Image Restoration](https://mlsanity.com/paper/2103.05961/) (2021)
- [Deep Shape-Texture Statistics for Completely Blind Image Quality Evaluation](https://mlsanity.com/paper/2401.08107/) (2024)
- [WTDUN: Wavelet Tree-Structured Sampling and Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2411.16336/) (2024)

## Abstract (arXiv)

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.