Statistical techniques for signal processing

The area of nonlinear edge-preserving robust smoothing was one area of focus for our research. In this area a dissertation was completed. We have been able to give deterministic and statistical characterizations of the performance of some useful types of nonlinear filters which may be thought of as arising from the classical robust estimates of location (Land M- estimates), and we have demonstrated their applicability in image processing. We are continuing to obtain new results in this area in our current work. In the area of nonparametric detection the case of narrowband signals in noise has been studied. We have established the natural counterparts of the sign-detection schemes for this class of signals. This material is currently being prepared for publication in a technical journal. A paper on quantization of data in narrowband signal detection was also published during the last grant year. On the subject of optimum quantization of data for signal detection (hypothesis testing) a comprehensive exposition has been written for publication as a chapter in a book to be published next year. These results on statistical optimization of quantization in detection systems are of considerable interest for digital implementations. Currently being revised for publication also is a paper on optimum quantization in matched filtering and smoothing of data. Finally, a paper on multi-input robust Wiener smoothing was also published during the last grant year.