Compound filter using the circular harmonic expansion.

A compound rotation-invariant filtering technique is developed which leads to sharp cross-correlation peaks for desired targets while suppressing random noise and unwanted target correlations. The basic compound filter structure is a filter bank consisting of several circular harmonic filters. The output image moduli from the filter bank are weighted and summed to form the final output image. In the design procedure, the weights are constrained so that the compound filter output has a peak value of 1 for the desired target. Measures of random noise and deterministic noise due to correlations with unwanted targets are minimized with respect to the weights. The SNR of the compound filter is, therefore, maximized. The weights constitute a real solution to a classical least-squares problem and are, therefore, unique. Some limits to the performance of the technique are discussed. Examples illustrating the filter performance are given. Optical, digital, and hybrid implementations of the compound filter are possible. Extensions of this work are discussed.