We study the problem of how to detect “interesting objects” appeared in a given image, I. Our approach is to treat it as a function approximation problem based on an over-redundant basis. Since the basis (a library of image templates) is over-redundant, there are infinitely many ways to decompose I. To select the “best” decomposition we first propose a global optimization procedure that considers a concave cost function derived from a “weighted Lpnorm” with 0 < p ≤ 1. This concave cost function selects as few coefficients as possible producing a sparse representation of the image and handle occlusions. However, it contains multiple local minima. We identify all local minima so that a global optimization is possible by visiting all of them. Secondly, because the number of local minima grows exponentially with the number of templates, we investigate a greedy “LpMatching Pursuit” strategy.