MIST: $l_0$ Sparse Linear Regression with Momentum

Goran Marjanovic, Magnus O. Ulfarsson, Alfred O. Hero III

Published 2014-09-25Version 1

Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the so-called $l_0$ norm. In this paper we develop a Momentumized Iterative Shrinkage Thresholding (MIST) algorithm for minimizing the resulting non-convex criterion and prove its convergence to a local minimizer. Simulations on large data sets show superior performance of the proposed method to other methods.