Sparse Coding for Natural Images Based on Pearson-Type VII Density Functions

Sparse coding is a method for finding a representation of natural images, in which each of the coefficients of the representation is only rarely significantly active. For extracting sparse structures in natural images adaptively, the prior probabilities over the coefficients are modeled with Pearson-type VII density functions, which can describe a wide class of super-Gaussian or sparse distributions, and can be adaptive to the input images by adjusting the scale and the steepness parameters flexibly in the density functions. Moreover, the derivatives of the sparseness cost function are continuous at each point of its domain, which is convenient for gradient techniques based learning algorithms. The performance of the flexible prior is demonstrated on a set of natural images.