Semi-Blind Source Separation with Learned Constraints
This work addresses the problem of obtaining physically interpretable decompositions in hyperspectral data analysis for domains like astrophysics, representing an incremental improvement by integrating learned priors into existing regularization frameworks.
The paper tackled the ill-posed problem of blind source separation in hyperspectral data by introducing a semi-supervised method that combines a projected alternating least-square algorithm with a learning-based regularization scheme using generative models to constrain the mixing matrix. The result was improved accuracy and reduced leakages between sources, as demonstrated on realistic astrophysical data under challenging conditions like strong noise and highly correlated spectra.
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.