Matrix approach to frame analysis of Gabor-type image representation

Meir Zibulski; Yehoshua Y. Zeevi

doi:10.1117/12.162072

1 November 1993 Matrix approach to frame analysis of Gabor-type image representation

Meir Zibulski, Yehoshua Y. Zeevi

Proceedings Volume 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing; (1993) https://doi.org/10.1117/12.162072
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

An approach for characterizing the properties of basis functions which constitute a finite scheme of discrete Gabor representation is presented in the context of oversampling. 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 the frame operator as a matrix-valued 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 eigenvalues 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.

Citation Download Citation

Meir Zibulski and Yehoshua Y. Zeevi "Matrix approach to frame analysis of Gabor-type image representation", Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); https://doi.org/10.1117/12.162072

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