Conventional and composite matched filters with error correction: a comparison

A common pattern recognition problem is finding a library object which most closely matches a received image. For additive white Gaussian input noise, optimal detection performance is obtained using a matched filter for each of the N possible library objects. The use of composite matched filters (CMFs) (also called synthetic discriminant functions or linear combination filters) is one technique of reducing the number of filters required for the recognition problem. For two-level composite matched filter outputs, the reduction is from N to Q = log(2) (N) filters. The CMF's performance, however, can be suboptimum. Using CMFs with bipolar (+1,-1) outputs, this paper examines the detection performance improvement obtained by using error correcting codes. Use of varying levels of error correction is shown to allow trade-off between detection probability and the number of bank filters. Also, we show that in the case of inexact processing, the CMF can perform better than the conventional matched filter.