Gabor representation with oversampling
Meir Zibulski, Yehoshua Y. Josh Zeevi · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
ABSTRACT An approach for characterizing the properties of the basis functions of the Gabor representation in the contextof oversampling is presented. The approach is based on the concept of frames and utilizes the Piecewise Zak Transform(PZT). The frame operator associated with the Gabor-type frame, the so-called Weyl-Heisenberg frame,is examined for a rational oversampling rate by representing the frame operator as a matrix-valued function in thePZT domain. Completeness and frame properties of the Gabor representation functions are examined in relation tothe properties of the matrix-valued function. The frame bounds are calculated by means of the eigenvalues of thematrix-valued function, and the dual frame, which is used in calculation of the expansion coefficients, is expressedby means of the inverse matrix. 1 INTRODUCTION Wavelets and Gabor-type representation have been found to be useful in effective representation and/or compression of images. The special case of Gaborian pyramid can, as such, be also considered as a wavelet which is most