Image representation using Hermite functions

We present a mathematical technique for analyzing images based on two-dimensional Hermite functions that are translated in both space and spatial frequency. Although the translated functions are not orthogonal, they do constitute a frame and hence can be used for image expansion. The technique has the practical advantage that fast algorithms based on the Zak transform (ZT) can be used to compute expansion coefficients. We describe properties of the ZT that are relevant to image representation and which allow us to use it both to compute expansion coefficients efficiently and to reconstruct images from them. Finally, we use a Hermite function frame to decompose and reconstruct a texture image. Received: 15 June 1993/Accepted in revised form: 22 December 1993