Blind Source Separation with Compressively Sensed Linear Mixtures

TL;DR

This paper introduces a novel method for blind source separation from compressively sensed mixtures, leveraging shared sparse representations and a geometric conjugate subgradient algorithm, enabling independent sampling and unsynchronized sensors.

Contribution

It combines compressive sensing with blind source separation under a shared sparse basis, proposing a scalable geometric optimization approach.

Findings

Demonstrates effective source separation with compressive measurements.

Outperforms several state-of-the-art methods in numerical experiments.

Handles large systems efficiently with the proposed algorithm.

Abstract

This work studies the problem of simultaneously separating and reconstructing signals from compressively sensed linear mixtures. We assume that all source signals share a common sparse representation basis. The approach combines classical Compressive Sensing (CS) theory with a linear mixing model. It allows the mixtures to be sampled independently of each other. If samples are acquired in the time domain, this means that the sensors need not be synchronized. Since Blind Source Separation (BSS) from a linear mixture is only possible up to permutation and scaling, factoring out these ambiguities leads to a minimization problem on the so-called oblique manifold. We develop a geometric conjugate subgradient method that scales to large systems for solving the problem. Numerical results demonstrate the promising performance of the proposed algorithm compared to several state of the art methods.