# Statistical Component Separation for Targeted Signal Recovery in Noisy Mixtures

arXiv: https://arxiv.org/abs/2306.15012 · HTML: https://mlsanity.com/paper/2306.15012/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 26 Jun 2023.

## Builds on (most cited first, 9 of 9)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Understanding Deep Convolutional Networks](https://mlsanity.com/paper/1601.04920/) (2016)
- [Image Denoising: The Deep Learning Revolution and Beyond -- A Survey Paper --](https://mlsanity.com/paper/2301.03362/) (2023)
- [Task adapted reconstruction for inverse problems](https://mlsanity.com/paper/1809.00948/) (2018)
- [Multiscale Sparse Microcanonical Models](https://mlsanity.com/paper/1801.02013/) (2018)
- [Maximum Entropy Models from Phase Harmonic Covariances](https://mlsanity.com/paper/1911.10017/) (2019)
- [Unearthing InSights into Mars: Unsupervised Source Separation with Limited Data](https://mlsanity.com/paper/2301.11981/) (2023)

## Abstract (arXiv)

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.