Joint deconvolution and unsupervised source separation for data on the sphere

TL;DR

This paper introduces SDecGMCA, a novel joint deconvolution and blind source separation algorithm tailored for large spherical data, with proven robustness and effectiveness through numerical experiments on toy and astronomical data.

Contribution

The paper presents a new regularized joint deconvolution and source separation method specifically designed for spherical data analysis.

Findings

Proves the accuracy depends on a new regularization scheme.

Demonstrates robustness and effectiveness on toy and real astronomical data.

Provides a scalable algorithm for large spherical datasets.

Abstract

Tackling unsupervised source separation jointly with an additional inverse problem such as deconvolution is central for the analysis of multi-wavelength data. This becomes highly challenging when applied to large data sampled on the sphere such as those provided by wide-field observations in astrophysics, whose analysis requires the design of dedicated robust and yet effective algorithms. We therefore investigate a new joint deconvolution/sparse blind source separation method dedicated for data sampled on the sphere, coined SDecGMCA. It is based on a projected alternate least-squares minimization scheme, whose accuracy is proved to strongly rely on some regularization scheme in the present joint deconvolution/blind source separation setting. To this end, a regularization strategy is introduced that allows designing a new robust and effective algorithm, which is key to analyze large spherical data. Numerical experiments are carried out on toy examples and realistic astronomical data.