Low rank prior and l0 norm to remove impulse noise in images

TL;DR

This paper introduces a novel image denoising method combining low rank prior and l0 norm optimization, solved via ADMM, demonstrating superior performance especially on images with weak or medium contrast.

Contribution

It proposes a new approach that integrates exact rank and l0 norm for impulse noise removal, using a Plug-and-Play ADMM framework with initial filtering.

Findings

Effective noise removal on weak and medium contrast images

Outperforms existing methods in denoising quality

Utilizes a non-convex optimization approach

Abstract

Patch-based low rank is an important prior assumption for image processing. Moreover, according to our calculation, the optimization of l0 norm corresponds to the maximum likelihood estimation under random-valued impulse noise. In this article, we thus combine exact rank and l0 norm for removing the noise. It is solved formally using the alternating direction method of multipliers (ADMM), with our previous patch-based weighted filter (PWMF) producing initial images. Since this model is not convex, we consider it as a Plug-and-Play ADMM, and do not discuss theoretical convergence properties. Experiments show that this method has very good performance, especially for weak or medium contrast images.