ABSTRACT

Multi-Window Gabor Schemes in Signal and Image Representations

M. Porat

Department of Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel
M. Zibulski
IBM Science & Technology, Haifa, Israel
Y.Y Zeevi
Department of Electrical Engineering, Technion - Israel Institute of Technology, Haifa, Israel
email: mp@ee.technion.ac.il

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. %We relate to three possible schemes, of undersampling, critical %sampling and oversampling. 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.