We discuss the problem of finding sparse representations of a class of signals. We formalize the problem and prove it is NP-complete both in the case of a single signal and that of multiple ones. Next we develop a simple approximation method to the problem and we show experimental results using artificially generated signals. Furthermore,we use our approximation method to find sparse representations of classes of real signals, specifically of images of pedestrians. We discuss the relation between our formulation of the sparsity problem and the problem of finding representations of objects that are compact and appropriate for detection and classification.
