Optimum Sidelobe-Reducing Invariant Matched Filters For Pattern Recognition

Abstract

Summary Composite matched filters, and Circular harmonic composite filters in particular, are associated with high sidelobes that degrade the recognition and discrimination performance of the filters. It is proposed to reduce the sidelobes of Circular harmonic composite filters by using coefficients that minimize the energy in the correlation plane, while still taking into account the constraints imposed on the filter by discrimination requirements. Experiments show that the results are much improved when a three-component CHC filter is used. The methods that have proven effective for combined translation and rotation invariance mostly involve the use of matched filters based on Circular harmonic components114. However the use of Circular harmonic component (CHC) filters are associated with certain problems, some of which are not completely solved. Such problems include the presence of high sidelobes and of the effect of surrounding backgrounds on the correlation peaks. Over the past few years, the performance of CHC filters have been improved by the use of a better choice of center of expansion6, the design of composite filters3'**' 7'13, of phase-only filters912, of principal component filters14, and various other modifications. The use of CHC composite filters in particular is associated with even higher sidelobes, which can be alleviated to some extent by using especially designed anti- sidelobe Previous approaches to reducing the sidelobe problem are mostly ad hoc methods, which are not easily amenable to analysis, so the value of such methods must be based on evaluation of their performance on scenes of interest. In this paper, we present an alternate approach to sidelobe reduction in rotation-invariant filters which is based on minimizing the energy in the correlation plane. Because high sidelobes contain a lot of energy, since they are usually quite broad, minimizing the energy in the correlation plane will increase the peak-to-sidelobe ratio.