Selecting the projection functions used in an iterative Gabor expansion

R. Neil Braithwaite; Michael P. Beddoes

doi:10.1117/12.162058

1 November 1993 Selecting the projection functions used in an iterative Gabor expansion

R. Neil Braithwaite, Michael P. Beddoes

Proceedings Volume 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing; (1993) https://doi.org/10.1117/12.162058
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

This paper discusses the selection of projection functions used in an iterative implementation of the Gabor expansion. We show that the optimal support-limited projection function corresponds to a truncated version of Bastiaans' biorthonormal projection function for the case of a harmonic lattice. For various support widths, the lower bound of the optimal convergence factor is calculated. It is shown that Gabor's original projection function, which corresponds to the central lobe of Bastiaans' biorthonormal projection function, is truncated too severely, producing a significant overlap with elementary functions from high frequency channels. As a result, the lower bound for the optimal convergence factor and the rate of convergence will approach zero as the signal bandwidth (and the highest frequency Gabor channel) is increased. This work also determines the lower bound of the optimal convergence factor for projection functions implemented using log-polar lattices. For both the harmonic and log-polar lattices, we investigate the trade-off between spread of convergence and the size of the projection function.

Citation Download Citation

R. Neil Braithwaite and Michael P. Beddoes "Selecting the projection functions used in an iterative Gabor expansion", Proc. SPIE 2034, Mathematical Imaging: Wavelet Applications in Signal and Image Processing, (1 November 1993); https://doi.org/10.1117/12.162058

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