Mixed geometry information regularization for image multiplicative denoising

TL;DR

This paper introduces a mixed geometry regularization model for multiplicative gamma image denoising, effectively removing noise while preserving edges and textures, and proposes efficient algorithms for its implementation.

Contribution

The paper proposes a novel mixed geometry information regularization model incorporating area and curvature terms, along with efficient additive operator splitting and SAV algorithms for denoising.

Findings

Effective noise removal with edge preservation

Better texture preservation without false details

Higher computational accuracy and efficiency

Abstract

This paper focuses on solving the multiplicative gamma denoising problem via a variation model. Variation-based regularization models have been extensively employed in a variety of inverse problem tasks in image processing. However, sufficient geometric priors and efficient algorithms are still very difficult problems in the model design process. To overcome these issues, in this paper we propose a mixed geometry information model, incorporating area term and curvature term as prior knowledge. In addition to its ability to effectively remove multiplicative noise, our model is able to preserve edges and prevent staircasing effects. Meanwhile, to address the challenges stemming from the nonlinearity and non-convexity inherent in higher-order regularization, we propose the efficient additive operator splitting algorithm (AOS) and scalar auxiliary variable algorithm (SAV). The unconditional stability possessed by these algorithms enables us to use large time step. And the SAV method shows higher computational accuracy in our model. We employ the second order SAV algorithm to further speed up the calculation while maintaining accuracy. We demonstrate the effectiveness and efficiency of the model and algorithms by a lot of numerical experiments, where the model we proposed has better features texturepreserving properties without generating any false information.