  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.
