Abstract

Sparse coding of time-varying natural images

Bruno Olshausen
University of California at Davis

Much work in image analysis has focussed on computing sparse decompositions of images. Usually the basis functions are designed by hand to meet certain mathematical criteria that are
believed to yield sparse representations of natural images. But the structure contained in natural images is rather complex and difficult to describe analytically. The approach we adopt here is to make no assumption about the form of the basis functions, and adapt them to the statistics of natural images so as to form
the sparsest representation. The learned basis functions tile the joint space of space and spatial-frequency in a manner that is more consistent with wavelets than with ridgelets or curvelets.When the basis functions are adapted to time-varying images they have similar spatial properties but translate over time with various velocities. I will also discuss recent efforts to learn shiftable basis functions from static images, which better captures the joint dependencies among basis function coefficients.