Extension of Sparse Randomized Kaczmarz Algorithm for Multiple Measurement Vectors
This work addresses a domain-specific problem in signal processing and computer vision, such as face recognition from video, but is incremental as it modifies an existing algorithm for a new application.
The authors tackled the problem of solving multiple measurement vector (MMV) problems with common sparse support by extending the randomized Kaczmarz algorithm, and their proposed method achieved better recovery and convergence rates than the state-of-the-art spectral projected gradient algorithm on real and synthetic datasets.
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.