Nonlocal Myriad Filters for Cauchy Noise Removal

TL;DR

This paper introduces a generalized myriad filter for Cauchy noise removal, providing efficient algorithms with proven convergence, and applies them within a nonlocal, unsupervised image denoising framework demonstrating excellent performance.

Contribution

It presents a novel generalized myriad filter for joint estimation of location and scale in Cauchy noise, with efficient algorithms and convergence proofs, applied to image denoising.

Findings

Algorithms show excellent denoising performance.

Methods are robust to parameter choices.

Significant improvement over existing techniques.

Abstract

The contribution of this paper is two-fold. First, we introduce a generalized myriad filter, which is a method to compute the joint maximum likelihood estimator of the location and the scale parameter of the Cauchy distribution. Estimating only the location parameter is known as myriad filter. We propose an efficient algorithm to compute the generalized myriad filter and prove its convergence. Special cases of this algorithm result in the classical myriad filtering, respective an algorithm for estimating only the scale parameter. Based on an asymptotic analysis, we develop a second, even faster generalized myriad filtering technique. Second, we use our new approaches within a nonlocal, fully unsupervised method to denoise images corrupted by Cauchy noise. Special attention is paid to the determination of similar patches in noisy images. Numerical examples demonstrate the excellent performance of our algorithms which have moreover the advantage to be robust with respect to the parameter choice.