# Semi-Blind Source Separation with Learned Constraints

arXiv: https://arxiv.org/abs/2209.13585 · HTML: https://mlsanity.com/paper/2209.13585/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 27 Sep 2022.

## Builds on (most cited first, 11 of 11)

- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [Source Separation with Deep Generative Priors](https://mlsanity.com/paper/2002.07942/) (2020)
- [Learning Independent Features with Adversarial Nets for Non-linear ICA](https://mlsanity.com/paper/1710.05050/) (2017)
- [Unsupervised Audio Source Separation using Generative Priors](https://mlsanity.com/paper/2005.13769/) (2020)
- [Deep Learning for space-variant deconvolution in galaxy surveys](https://mlsanity.com/paper/1911.00443/) (2019)
- [Joint deconvolution and unsupervised source separation for data on the sphere](https://mlsanity.com/paper/2012.12740/) (2020)

## Abstract (arXiv)

Blind source separation (BSS) algorithms are unsupervised methods, which are the cornerstone of hyperspectral data analysis by allowing for physically meaningful data decompositions. BSS problems being ill-posed, the resolution requires efficient regularization schemes to better distinguish between the sources and yield interpretable solutions. For that purpose, we investigate a semi-supervised source separation approach in which we combine a projected alternating least-square algorithm with a learning-based regularization scheme. In this article, we focus on constraining the mixing matrix to belong to a learned manifold by making use of generative models. Altogether, we show that this allows for an innovative BSS algorithm, with improved accuracy, which provides physically interpretable solutions. The proposed method, coined sGMCA, is tested on realistic hyperspectral astrophysical data in challenging scenarios involving strong noise, highly correlated spectra and unbalanced sources. The results highlight the significant benefit of the learned prior to reduce the leakages between the sources, which allows an overall better disentanglement.