An Analysis of Gabor Detection

An elementary function that is now commonly referred to Gabor function, Gabor filter and Gabor wavelet was derived from uncertainty relation for information by Gabor to overcome the representation limit of Fourier analysis. Analyzing a signal by a Gabor filter in terms of convolution or spatial filtering, two pieces of information—phase and magnitude—can be obtained. In the paper, Gabor filter is considered as a Gabor atom detector. This analysis demonstrates that when the k-value defined as 2 2 / nr ni g g k = , where gnr and gni are respectively the real and imaginary parts of a Gabor filter gn, is close to one, the target phase can be estimated by Gabor phase and the target magnitude can be estimated by Gabor magnitude. However, when the k-value decreases, the quality of this approximation also decreases. The corresponding error bounds are derived.