Image Recognition with

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 innnitely many ways to decompose I. To select the \best" decomposition we rst propose a global optimization procedure that considers a concave cost function derived from a \weighted L p norm" with 0 < p 1. This concave cost function selects as few coeecients 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 \L p Matching Pursuit" strategy.