Formulating Beurling LASSO for Source Separation via Proximal Gradient Iteration
This work addresses a specific problem in source separation for researchers in signal processing, but it appears incremental as it focuses on an algorithmic formulation without claiming major breakthroughs.
The authors tackled the algorithmic challenge of applying Beurling LASSO to continuous convolutional source separation by proposing a formulation that avoids explicit computation of measures and uses the duality transform of the proximal mapping.
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.