A Study of Image Compression with Backpropagation

Abstract

Backpropagation is one possible algorithm used to achieve image compression with a multi-layer neural net [l]. Associated with a quadratic cost function in a linear case, it is nothing but an indirect way to compress images with the Karhunen-Loève method [2]. So, in this case, this algorithm brings no improvement. However, the knowledge of the optimal solution helps us to study in detail, how the backpropagation algorithm solves the compression problem. We show that the convergence of the learning process can be accelerated by setting some constraints on the weights. The error function is then minimized for an unique value around which it is strictly convex.

In order to improve the visual appearance of restored images, we use the same algorithm associated to other cost functions (p-Hölder norms). Unlike the quadratic case, the theoretical optimal solution for the p-Hölder norms (p≠2) is not known, and backpropagation is shown to provide a relevant tool to compute the optimal solution.