Multi-window Gabor schemes in signal and image representations

Abstract

Motivated by biological vision, schemes of signal and image representation by localized Gabor-type functions are introduced and analyzed. These schemes, suitable for information representation in a combined frequency-position space are investigated through signal decomposition into a set of elementary functions. Utilizing the Piecewise Zak transform (PZT), the theory of the multi-window approach is given in detail based on the mathematical concept of frames. The advantages of using more than a single window are analyzed and discussed. Applications to image processing and computer vision are presented with regard to texture images, and considered in the context of two typical tasks: image representation by partial information and pattern recognition. In both cases the results indicate that the multi-window approach is efficient and superior in major aspects to previously available methods. It is concluded that the new multi-window Gabor approach could be integrated efficiently into practical techniques of signal and image representation.