Formulating Beurling LASSO for Source Separation via Proximal Gradient Iteration

TL;DR

This paper introduces a novel formulation of Beurling LASSO for source separation that leverages duality transforms to avoid explicit measure computation, enabling more efficient algorithms.

Contribution

It presents a new approach to continuous source separation using Beurling LASSO with proximal gradient iteration, bypassing measure parametrization.

Findings

Efficient algorithm for continuous source separation

Avoids explicit measure computation

Utilizes duality transform of proximal mapping

Abstract

Beurling LASSO generalizes the LASSO problem to finite Radon measures regularized via their total variation. Despite its theoretical appeal, this space is hard to parametrize, which poses an algorithmic challenge. We propose a formulation of continuous convolutional source separation with Beurling LASSO that avoids the explicit computation of the measures and instead employs the duality transform of the proximal mapping.