A new framework for utilizing side information in sparse representation

Abstract

An underdetermined system of linear equation has infinitely number of answers. To find a specific solution, regularization method is used. For this propose, we define a cost function based on desired features of the solution and that answer with the best matches to these function is selected as the desired solution. In case of sparse solution, zero-norm function is selected as the cost function. In many engineering cases, there is side information which are omitted because of the zero-norm function. Finding a way to conquer zero-norm function limitation, will help to improve estimation of the desired parameter. In this regard, we utilize maximum a posterior (MAP) estimation and modify the prior information such that both sparsity and side information are utilized. As a consequence, a framework to utilize side information into sparse representation algorithms is proposed. We also test our proposed framework in orthogonal frequency division multiplexing (OFDM) sparse channel estimation problem which indicates, by utilizing our proposed system, the performance of the system improves and fewer resources are required for estimating the channel.