Structure of the Gabor matrix and efficient numerical algorithms for discrete Gabor expansions

Sigang Qiu; Hans Georg Feichtinger

doi:10.1117/12.185874

16 September 1994 Structure of the Gabor matrix and efficient numerical algorithms for discrete Gabor expansions

Sigang Qiu, Hans Georg Feichtinger

Proceedings Volume 2308, Visual Communications and Image Processing '94; (1994) https://doi.org/10.1117/12.185874
Event: Visual Communications and Image Processing '94, 1994, Chicago, IL, United States

Abstract

The standard way to obtain suitable coefficients for the (non-orthogonal) Gabor expansion of a general signal for a given Gabor atom g and a pair of lattice constants in the (discrete) time/frequency plane, requires to compute the dual Gabor window function g^- first. In this paper, we present an explicit description of the sparsity, the block and banded structure of the Gabor frame matrix G. On this basis efficient algorithms are developed for computing g^- by solving the linear equation g^- * G equals g with the conjugate- gradients method. Using the dual Gabor wavelet, a fast Gabor reconstruction algorithm with very low computational complexity is proposed.

Citation Download Citation

Sigang Qiu and Hans Georg Feichtinger "Structure of the Gabor matrix and efficient numerical algorithms for discrete Gabor expansions", Proc. SPIE 2308, Visual Communications and Image Processing '94, (16 September 1994); https://doi.org/10.1117/12.185874

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