Conjoint image representation with a weighted Zak transform

Abstract

An image-representation technique is described that uses a window function that provides good localization in both space and spatial frequency. The window function is obtained by weighting of the Zak transform (ZT) of a Gaussian. The weighting procedure eliminates the zero in the ZT, thus permitting efficient and stable computation of expansion coefficients with respect to the derived window function. Since the window function is related to Gabor functions and, in addition, resembles a visual receptive field, it may also be useful in visual representation and modeling.