Recursive Gabor filtering

Author

Young, Ian T. ; Van Vliet, Lucas J. ; Van Ginkel, Michael

Author_Institution

Dept. of Appl. Phys., Delft Univ. of Technol., Netherlands

Volume

50

Issue

11

fYear

2002

fDate

11/1/2002 12:00:00 AM

Firstpage

2798

Lastpage

2805

Abstract

We present a stable, recursive algorithm for the Gabor (1946) filter that achieves-to within a multiplicative constant-the fastest possible implementation. For a signal consisting of N samples, our implementation requires O(N) multiply-and-add (MADD) operations, that is, the number of computations per input sample is constant. Further, the complexity is independent of the values of σ, and ω in the Gabor kernel, and the coefficients of the recursive equation have a simple, closed-form solution given σ and ω. Our implementation admits not only a "forward" Gabor filter but an inverse filter that is also O(N) complexity.

Keywords

IIR filters; communication complexity; filtering theory; image processing; multidimensional signal processing; numerical stability; recursive filters; two-dimensional digital filters; wavelet transforms; Gabor kernel; Gabor wavelets; IIR Gabor filter; algorithm complexity; closed-form solution; forward Gabor filter; image processing; inverse filter; multidimensional filtering; multidimensional signal processing; multiply-and-add operations; recursive Gabor filtering; recursive algorithm; recursive equation coefficients; stable algorithm; two-dimensional filtering; Closed-form solution; Equations; Filtering; Frequency; Gabor filters; IIR filters; Information analysis; Kernel; Signal analysis; Spectrogram;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2002.804095

Filename

1041037