22 October 1993 Matrix algebra approach to Gabor-type image representation
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Proceedings Volume 2094, Visual Communications and Image Processing '93; (1993) https://doi.org/10.1117/12.157934
Event: Visual Communications and Image Processing '93, 1993, Cambridge, MA, United States
Abstract
Properties of basis functions which constitute a finite scheme of discrete Gabor representation are investigated. The approach is based on the concept of frames and utilizes the Piecewise Finite Zak Transform (PFZT). The frame operator associated with the Gabor-type frame is examined by representing it as a matrix-values function in the PFZT domain. The frame property of the Gabor representation functions are examined in relation to the properties of the matrix-valued function. The frame bounds are calculated by means of the eignevalues of the matrix-valued function, and the dual frame, which is used in calculation of the expansion coefficients, is expressed by means of the inverse matrix. DFT-based algorithms for computation of the expansion coefficients, and for the reconstruction of signals from these coefficients are generalized for the case of oversampling of the Gabor space. It is illustrated by an example that a better reconstruction is obtained in from the same number of coefficients in the case of oversampling.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Meir Zibulski, Yehoshua Y. Zeevi, "Matrix algebra approach to Gabor-type image representation", Proc. SPIE 2094, Visual Communications and Image Processing '93, (22 October 1993); doi: 10.1117/12.157934; https://doi.org/10.1117/12.157934
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