  The Kaczmarz algorithm is popular for iteratively solving an overdetermined
system of linear equations. The traditional Kaczmarz algorithm can approximate
the solution in few sweeps through the equations but a randomized version of
the Kaczmarz algorithm was shown to 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 were multiple-measurements are available. In
this work, the objective is to solve a multiple measurement vector problem with
common sparse support by modifying the 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 have better
recovery and convergence rate than the MMV version of spectral projected
gradient algorithm under fairness constraints.
