Learning Overcomplete Representations with a Generalized Gaussian Prior

Overcomplete representations have been advocated because they allow a basis to better approximate the underlying statistical density of the data which can lead to representations that better capture the underlying structure in the data. The prior distributions for the coefficients of these models, however, are assumed to be fixed, not adaptive to the data, and hereby inaccurate. Here we describe a method for learning overcomplete representations with a generalized Gaussian prior, which can fit a broader range of statistical distributions by varying the value of the steepness parameter β. Using this distribution in overcomplete representations, empirical results were obtained for the blind source separation of more sources than mixtures, which show that the accuracy of the density estimation is improved.