Unrolling PALM for sparse semi-blind source separation

TL;DR

This paper introduces LPALM, an unrolled version of PALM for sparse semi-blind source separation, which learns hyperparameters and handles variable dictionaries, improving efficiency and accuracy in astrophysical imaging.

Contribution

The work develops LPALM, a novel unrolled PALM algorithm that learns hyperparameters and adapts to changing dictionaries for semi-blind source separation.

Findings

LPALM requires up to 10^4-10^5 times fewer iterations than PALM.

LPALM improves separation quality over traditional PALM.

LPALM outperforms other unrolled methods in semi-blind scenarios.

Abstract

Sparse Blind Source Separation (BSS) has become a well established tool for a wide range of applications - for instance, in astrophysics and remote sensing. Classical sparse BSS methods, such as the Proximal Alternating Linearized Minimization (PALM) algorithm, nevertheless often suffer from a difficult hyperparameter choice, which undermines their results. To bypass this pitfall, we propose in this work to build on the thriving field of algorithm unfolding/unrolling. Unrolling PALM enables to leverage the data-driven knowledge stemming from realistic simulations or ground-truth data by learning both PALM hyperparameters and variables. In contrast to most existing unrolled algorithms, which assume a fixed known dictionary during the training and testing phases, this article further emphasizes on the ability to deal with variable mixing matrices (a.k.a. dictionaries). The proposed Learned PALM (LPALM) algorithm thus enables to perform semi-blind source separation, which is key to increase the generalization of the learnt model in real-world applications. We illustrate the relevance of LPALM in astrophysical multispectral imaging: the algorithm not only needs up to $10^4-10^5$ times fewer iterations than PALM, but also improves the separation quality, while avoiding the cumbersome hyperparameter and initialization choice of PALM. We further show that LPALM outperforms other unrolled source separation methods in the semi-blind setting.