Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization

TL;DR

This paper introduces MIDAL, a novel method for removing multiplicative noise in coherent imaging systems by transforming the problem into a constrained additive form and solving it with augmented Lagrangian techniques, achieving state-of-the-art results.

Contribution

The paper presents a new approach combining logarithmic transformation, variable splitting, and augmented Lagrangian optimization for effective multiplicative noise removal.

Findings

MIDAL outperforms existing methods in speed and accuracy.

The approach effectively handles non-Gaussian multiplicative noise.

Experimental results demonstrate superior denoising performance.

Abstract

Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of difficulties with respect to the standard Gaussian additive noise scenario: (1) the noise is multiplied by (rather than added to) the original image; (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of multiplicative noise models preclude the direct application of most state-of-the-art algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (log-likelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a total variation or wavelet-based regularizer/prior). In this paper, we address these difficulties by: (1) converting the multiplicative model into an additive one by taking logarithms, as proposed by some other authors; (2) using variable splitting to obtain an equivalent constrained problem; and (3) dealing with this optimization problem using the augmented Lagrangian framework. A set of experiments shows that the proposed method, which we name MIDAL (multiplicative image denoising by augmented Lagrangian), yields state-of-the-art results both in terms of speed and denoising performance.