Sparse Representation of Multiple Signals

We discuss the problem of nding 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 arti cially generated signals. Furthermore,we use our approximation method to nd sparse representations of classes of real signals, speci cally of images of pedestrians. We discuss the relation between our formulation of the sparsity problem and the problem of nding representations of objects that are compact and appropriate for detection and classi cation. Copyright c Massachusetts Institute of Technology, 1997 This report describes research done within the Arti cial Intelligence Laboratory and the Center for Biological and Computational Learning in the Department of Brain and Cognitive Sciences at the Massachusetts Institute of Technology. This research is sponsored by grants from MURI N00014-75-0600.