Sparse representations for image decomposition with occlusions

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problem based on an over-redundant basis, and also account for occlusions, where the basis superposition principle is no longer valid. Since the basis (a library of image templates) is over-redundant, there are infinitely many ways to decompose I. We are motivated to select a sparse/compact representation of I, and to account for occlusions and noise. We then study a greedy and iterative 'weighted L^p Matching Pursuit' strategy, with 0 < p < 1. We use an L^p result to compute a solution, select the best template, at each stage of the pursuit.