Recently, the Line Search A-Function (LSAF) was introduced as a technique that generalizes Extended Baum-Welch (EBW) algorithm for functions of continuous probability densities. It was shown that LSAF provides a unified scheme for a large class of optimization problems that involve discriminant objective functions of different probability densities or sparse representation objective functions such as Approximate Bayesian Compressive Sensing. In this paper, we show that a discrete EBW recursion (that was initially developed to optimize functions of discrete distributions) also fits the scope of LSAF technique. We demonstrate the utility and robustness of the technique for discrete distributions thru the experimental set up of a TIMIT phone classification task using a Convex Hull Sparse Representation approach with different Lq regularization (q being any positive number). Copyright © 2011 ISCA.