Recursive Gabor filtering

Abstract

In this paper, we present a stable, recursive algorithm for the Gabor 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 sigma and omega in the Gabor kernel, and the coefficients of the recursive equation have a simple, closed-form solution given sigma and omega. Our implementation admits not only a ¿forward¿ Gabor filter but an inverse filter that is also O(N ) complexity.
Index Terms¿Gabor filtering, Gabor wavelets, IIR filters, multidimensional filtering, recursive filtering.