Extension of Sparse Randomized Kaczmarz Algorithm for Multiple Measurement Vectors

Abstract

The Kaczmarz algorithm is popular for iteratively solving an over determined system of linear equations. Randomized version of the Kaczmarz algorithm can converge exponentially and independent of number of equations. Recently an algorithm for finding sparse solution to a linear system of equations has been proposed based on weighted randomized Kaczmarz algorithm. These algorithms solves single measurement vector problem, however there are applications where multiple-measurements are available. In this work, the objective is to solve a multiple measurement vector problem with common sparse support by modifying the sparse randomized Kaczmarz algorithm. We have also modeled the problem of face recognition from video as the multiple measurement vector problem and solved using our proposed technique. We have compared the proposed algorithm with state-of-art spectral projected gradient algorithm for multiple measurement vectors on both real and synthetic datasets. The Monte Carlo simulations confirms that our proposed algorithm has better recovery and convergence rate than the MMV version of spectral projected gradient algorithm under fairness constraints.