Sparse Representation in Redundant Systems

CSIC Building (#406), Seminar Room 4122.
Directions: home.cscamm.umd.edu/directions

Redundancy, Sparsity, and Nonlinear Approximation via Time-Frequency Representations

Dr. Patrick Wolfe

Division of Engineering and Applied Sciences at Harvard University

Abstract:   As of late, the engineering and computer science literatures have seen a vast increase in applications of sparsity to statistical signal processing problems. In this talk I will describe a framework for understanding these apparently disparate approaches from a Bayesian point of view, and present an overview of statistical model-based techniques for audio signal processing using time-frequency representations. In contrast to the orthonormal transformations employed in many areas of signal and image analysis, audio signals have traditionally been analyzed, modified, and reconstructed by way of overcomplete time-frequency representations--i.e., frames. Whereas the theory of frames has most often concerned the minimal l-2 norm reconstruction coefficients in a particular scenario, I describe a regularization approach aimed at estimating a sparse set of synthesis coefficients directly from the (audio) time series under consideration.