Semi-Blind Source Separation with Learned Constraints

TL;DR

This paper introduces sGMCA, a semi-supervised blind source separation method that leverages learned generative models to improve accuracy and interpretability in hyperspectral data analysis, especially under challenging noisy conditions.

Contribution

The paper proposes a novel BSS algorithm that constrains the mixing matrix to a learned manifold, enhancing separation quality and interpretability compared to traditional methods.

Findings

Improved source disentanglement in noisy hyperspectral data.

Significant reduction in source leakage using learned priors.

Enhanced performance in scenarios with correlated spectra and unbalanced sources.

Abstract

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.