# Joint Multichannel Deconvolution and Blind Source Separation

## TL;DR

This paper introduces DecGMCA, a novel joint deconvolution and blind source separation method that effectively handles instrumental effects in multichannel imaging, with promising results on simulated astrophysical data.

## Contribution

DecGMCA is a new approach combining sparse modeling and an efficient algorithm to jointly solve deconvolution and BSS, addressing limitations of existing methods.

## Key findings

- DecGMCA performs well on simulated data.
- Jointly solving BSS and deconvolution improves results.
- Effective on radio-interferometric simulations.

## Abstract

Blind Source Separation (BSS) is a challenging matrix factorization problem that plays a central role in multichannel imaging science. In a large number of applications, such as astrophysics, current unmixing methods are limited since real-world mixtures are generally affected by extra instrumental effects like blurring. Therefore, BSS has to be solved jointly with a deconvolution problem, which requires tackling a new inverse problem: deconvolution BSS (DBSS). In this article, we introduce an innovative DBSS approach, called DecGMCA, based on sparse signal modeling and an efficient alternative projected least square algorithm. Numerical results demonstrate that the DecGMCA algorithm performs very well on simulations. It further highlights the importance of jointly solving BSS and deconvolution instead of considering these two problems independently. Furthermore, the performance of the proposed DecGMCA algorithm is demonstrated on simulated radio-interferometric data.