Localized measurement of emergent image frequencies by Gabor wavelets

The authors derive, implement, and demonstrate a computational approach for the measurement of emergent image frequencies. Measuring emergent signal frequencies requires spectral measurements accurate in both frequency and time or space, conflicting requirements that are shown to be balanced by a generalized uncertainty relationship. Such spectral measurements can be obtained from the responses of multiple wavelet-like channel filters that sample the signal spectrum, and that yield a locus of possible solutions for each locally emergent frequency. It is shown analytically that this locus of solutions is maximally localized in both space and frequency if the channel filters used are Gabor wavelets. A constrained solution is obtained by imposing a stabilizing term that develops naturally from the assumptions on the signal. The measurement of frequencies is then cast as an ill-posed extremum problem regularized by the stabilizing term, leading to an iterative constraint propagation algorithm. The technique is demonstrated by application to a variety of 2-D textured images.<>