A First Step to Convolutive Sparse Representation

TL;DR

This paper introduces an algorithm that finds the sparsest shifted version of a signal within an overcomplete dictionary, extending sparse decomposition to include shifts and demonstrating effective performance through experiments.

Contribution

It presents a novel algorithm for simultaneous shift estimation and sparse representation in an extended sparse decomposition framework.

Findings

Algorithm effectively finds the required shift and sparse representation.

Experimental results demonstrate strong performance of the proposed method.

Extends sparse decomposition to handle shifted signals.

Abstract

In this paper an extension of the sparse decomposition problem is considered and an algorithm for solving it is presented. In this extension, it is known that one of the shifted versions of a signal s (not necessarily the original signal itself) has a sparse representation on an overcomplete dictionary, and we are looking for the sparsest representation among the representations of all the shifted versions of s. Then, the proposed algorithm finds simultaneously the amount of the required shift, and the sparse representation. Experimental results emphasize on the performance of our algorithm.