Recursive Gabor Filtering

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 samples, our implementation requires ( ) 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 and in the Gabor kernel, and the coefficients of the recursive equation have a simple, closed-form solution given and . Our implementation admits not only a “forward” Gabor filter but an inverse filter that is also ( ) complexity.