Multiscale hierarchical decomposition methods for images corrupted by multiplicative noise

TL;DR

This paper introduces multiscale hierarchical decomposition methods tailored for removing multiplicative noise from images, offering new models with proven convergence and practical stopping criteria, validated through extensive experiments.

Contribution

It adapts and refines multiscale hierarchical decomposition methods specifically for multiplicative noise removal, including theoretical analysis and new stopping rules.

Findings

Models effectively denoise and deblur images with multiplicative noise

Proposed methods recover multiple image scales, revealing additional features

Numerical experiments demonstrate superior performance over existing approaches

Abstract

Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new multiplicative noise removing models to the MHDM form. On the basis of previous work, we further present a tight and a refined version of the corresponding multiplicative MHDM. We discuss existence and uniqueness of solutions for the proposed models, and additionally, provide convergence properties. Moreover, we present a discrepancy principle stopping criterion which prevents recovering excess noise in the multiscale reconstruction. Through comprehensive numerical experiments and comparisons, we qualitatively and quantitatively evaluate the validity of all proposed models for denoising and deblurring images degraded by multiplicative noise. By construction, these multiplicative multiscale hierarchical decomposition methods have the added benefit of recovering many scales of an image, which can provide features of interest beyond image denoising.