The finite Zak transform: An efficient tool for image representation and analysis

Authors:
Yehoshua Y. Zeevi;Izidor Gertner
Affiliations:
Technion-Israel Institute of Technology, Technion City, Haifa, 32000, Israel;Vision and Parallel Computations Laboratory, CAIP Center, Rutgers University, Piscataway, New Jersey, 08855, USA
Venue:
Journal of Visual Communication and Image Representation
Year:
1992

Citing 3
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Abstract

A mathematical approach to image representation and analysis is presented. The formalism is based on the finite Zak transform (FZT), which provides an important tool for the analysis of images that by their very nature are spatially nonstationary. The discrete Zak transform is extended to two spatial dimensions, and fundamental properties of the two-dimensional FZT are discussed, emphasizing the direct relationship that exists between the Zak transform and the Cooley-Tukey FFT algorithm. Subsampling and interpolation are considered in the context of various mappings into the combined space. The two-dimensional FZT is applied to image representation and image analysis in computation of the Gabor expansion coefficients with arbitrary resolution. A technique for stable reconstruction is implemented and illustrated.