LCS: A Learnlet-Based Sparse Framework for Blind Source Separation

TL;DR

LCS is a hybrid deep learning framework that uses a learned wavelet-like transform to improve blind source separation in astrophysics, outperforming traditional methods on synthetic and real data.

Contribution

We introduce the Learnlet Component Separator (LCS), a novel hybrid BSS framework combining classical sparsity with deep learning for improved astrophysical signal separation.

Findings

LCS achieves about 5 dB higher separation gain than state-of-the-art methods.

LCS effectively decomposes multi-channel astrophysical observations.

The learned transform enhances interpretability and adaptability in BSS.

Abstract

Blind source separation (BSS) plays a pivotal role in modern astrophysics by enabling the extraction of scientifically meaningful signals from multi-frequency observations. Traditional BSS methods, such as those relying on fixed wavelet dictionaries, enforce sparsity during component separation, but may fall short when faced with the inherent complexity of real astrophysical signals. In this work, we introduce the Learnlet Component Separator (LCS), a novel BSS framework that bridges classical sparsity-based techniques with modern deep learning. LCS utilizes the Learnlet transform: a structured convolutional neural network designed to serve as a learned, wavelet-like multiscale representation. This hybrid design preserves the interpretability and sparsity, promoting properties of wavelets while gaining the adaptability and expressiveness of learned models. The LCS algorithm integrates this learned sparse representation into an iterative source separation process, enabling effective decomposition of multi-channel observations. While conceptually inspired by sparse BSS methods, LCS introduces a learned representation layer that significantly departs from classical fixed-basis assumptions. We evaluate LCS on both synthetic and real datasets, demonstrating superior separation performance compared to state-of-the-art methods (average gain of about 5 dB on toy model examples). Our results highlight the potential of hybrid approaches that combine signal processing priors with deep learning to address the challenges of next-generation cosmological experiments.