Hard Thresholding based Stochastic Robust Algorithm for Multiple Measurement Vectors

In this paper, we propose a Hard Thresholding (HT) based robust algorithm for large scale Multiple Measurement Vectors (MMV) problem in Compressed Sensing. The proposed MStoLIHT algorithm is based upon Stochastic Gradient Descent (SGD) and employs the Lorentzian norm of residual as the underlying cost function which provides robustness against impulsive errors in the measurements. Each iteration of the MStoLIHT algorithm consists of multiple subiterations. At each iteration, only a block of rows of the sensing matrix is used for carrying out the update, and at each subiteration, only few of the columns of the estimated data matrix are updated based on the SGD and the HT strategies. At the end of subiterations, another HT operation is performed ensuring the row sparsity in the estimated data matrix. Extensive numerical simulations are carried out, which indicate that by updating the data matrix in blocks of columns followed by HT operation, the performance in terms of probability of support recovery is improved when compared to its deterministic counterpart. It is further observed that the MStoLIHT algorithm outperforms other existing algorithms for the MMV problem in literature.