Recovery of Linearly Mixed sparse Sources From Multiple Measurement Vectors Using l1 Minimization

Abstract

Multiple measurement vector (MMV) enables joint sparse recovery which can be applied in wide range of applications. Traditional MMV algorithms assume that the solution has independent columns or correlation among the columns. This assumption is not accurate for applications like signal estimation in photoplethysmography (PPG). In this paper, we consider a structure for the solution matrix decomposed into a sparse matrix with independent columns and a square mixing matrix. Based on this structure, we find the uniqueness condition for l 1 minimization. Moreover, an algorithm is proposed that provides a new cost function based on the new structure. It is shown that the new structure increases the recovery performance especially in low number of measurements.