Convex/Schur-Convex (CSC) Log-Priors and Sparse Coding

The "folk theorem" that sparsity inducing priors should be supergaussian can be rigorously stated in the low-noise limit, assuming the validity of a particular stochastic generative model. For the assumed model it is shown that supergaussianess is necessary, but not sufficient, for sparse signal coding when a maximum a posterior (MAP) coding is found. 1 Introduction It has been noted by a variety of investigators in several different research domains (human vision, signal processing, etc) that a generative model appropriate for understanding sparse coding and Independent Component Analysis (ICA) is given by the system of equations, y = Ax + ; (1) where y is an observed signal vector, x is an unobserved ("blind") source vector, the columns of A form an overcomplete dictionary, and is a measurement noise vector which is independent of the source. As will be shown below, equation (1) is profitably interpreted within a Bayesian framework. The components, x[k], k = 1; \Delta \Delta \De..