Mixed geometry information regularization for image multiplicative denoising
Shengkun Yang, Zhichang Guo, Jia Li, Fanghui Song, Wenjuan Yao
TL;DR
This work tackles multiplicative denoising under gamma-distributed noise by introducing a mixed geometry information model that fuses a minimal surface (area) term with a curvature term, augmented by a gray level indicator to adapt to signal strength. The energy functional $E(u)$ combines these priors with a fidelity term, and its gradient flow is solved using unconditionally stable numerical schemes: additive operator splitting (AOS) and scalar auxiliary variable (SAV), with the latter offering higher accuracy and faster convergence, especially in its second-order form. The authors provide detailed discretizations, stability analyses, and adaptive time-stepping strategies, and demonstrate via extensive experiments on synthetic, SAR-like, and ultrasound-like data that the proposed approach preserves edges and textures while suppressing multiplicative noise and avoiding staircasing more effectively than several state-of-the-art methods. The method shows promise for real imaging systems dealing with coherent, non-Gaussian speckle noise, offering robust performance and practical scalability for high-quality image restoration.
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.