Generative and Filtering Approaches for Overcomplete Representations

We investigate the properties of the generative and filtering approach to overcomplete representations. A Mixture of Gaussian (MoG) density model is used to derive estimation rules for an energy based model, which estimate the filtering matrix, as well as a generative model which estimate the mixing matrix. In the light of two different source priors ??? a spherical MoG and an independent MoG ??? we reveal how those two seemingly different approaches can be understood. We also provide a new zero noise case which enables a closer comparison of the generative model to the energy based model.