Statistical Component Separation for Targeted Signal Recovery in Noisy Mixtures

Published: 28 Feb 2024, Last Modified: 28 Feb 2024Accepted by TMLREveryoneRevisionsBibTeX
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.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: Camera ready version incorporating revisions from the reviewing process.
Assigned Action Editor: ~Stephen_Becker1
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Number: 1740