Statistical Component Separation for Targeted Signal Recovery in Noisy Mixtures

TL;DR

This paper introduces a statistical component separation method that recovers specific signal properties from noisy mixtures, demonstrating improved descriptor recovery and promising denoising results, especially with wavelet descriptors and a diffusive algorithm.

Contribution

The work presents a novel statistical matching approach for targeted signal property recovery, with extensions to a diffusive algorithm for enhanced image denoising.

Findings

Better recovery of target descriptors than standard methods in most cases

Surprisingly good full signal reconstruction performance

Diffusive algorithm improves denoising under certain conditions

Abstract

Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on recovering a predefined set of statistical descriptors of a target signal from a noisy mixture. Assuming access to samples of the noise process, we investigate a method devised to match the statistics of the solution candidate corrupted by noise samples with those of the observed mixture. We first analyze the behavior of this method using simple examples with analytically tractable calculations. Then, we apply it in an image denoising context employing 1) wavelet-based descriptors, 2) ConvNet-based descriptors on astrophysics and ImageNet data. In the case of 1), we show that our method better recovers the descriptors of the target data than a standard denoising method in most situations. Additionally, despite not constructed for this purpose, it performs surprisingly well in terms of peak signal-to-noise ratio on full signal reconstruction. In comparison, representation 2) appears less suitable for image denoising. Finally, we extend this method by introducing a diffusive stepwise algorithm which gives a new perspective to the initial method and leads to promising results for image denoising under specific circumstances.