Learning Sparse Representations Using a Parametric Cauchy Density*

摘要

For extracting sparse structures in images adaptively, the prior probabilities over the coefficients are modeled with a flexible parametric Cauchy density, which can describe a class of super-Gaussian distributions by varying the steepness and the scale parameters in the density function. The derivatives of the sparseness cost function are continuous at each point of its domain, which is convenient for gradient techniques based learning algorithms, and may provide a better approximation of the volume contribution from the prior. The performance of the flexible prior is demonstrated on a set of natural images.