## EECS CSPL SEMINAR SERIES

FALL TERM 1996

Robert Nowak
### Department of Electrical Engineering, Michigan State University

### rnowak@egr.msu.edu

Tuesday, November 19, 1996

4:30-5:30 pm

1003 EECS

### Optimal Signal Estimators Based on the Method of
Cross-Validation

Abstract -

An optimal, data-adaptive estimator of a deterministic
signal in noise is introduced in this talk. The methods of penalized
least squares and cross-validation balance the trade-off between bias
and variance and produce a closed form expression for the estimator.
The estimator is simultaneously optimal in a small-sample, predictive
sum of squares sense and asymptotically optimal in the mean square
sense. The framework developed in the talk enables us to assess the
effect of using different signal bases in the estimation problem. We
introduce the notion of a "matched basis" for a signal or class of
signals.
We show that an estimator designed with a matched basis
performs significantly better than an estimator designed
with an arbitrary basis.
We apply the new
estimator to nuclear medicine imaging. The quality of the resulting
images is much better than standard image estimates, in both visual
and mean square error senses. Moreover, experiments have shown that,
using the new estimate, we can reduce the acquisition time by a factor
of two and still retain high image quality.

Biosketch -

Robert Nowak received the B.S. (with highest distinction), M.S., and
Ph.D. degrees in electrical engineering from the University of
Wisconsin-Madison in 1990, 1992, and 1995, respectively. He held a
Wisconsin Alumni Research Foundation Fellowship while working on the
M.S. degree. While working towards the Ph.D. degree, he was a Rockwell
International Doctoral Fellow. He has also worked at General Electric
Medical Systems.

During 1995-1996 he was a Postdoctoral Research Fellow at Rice
University, Houston TX. Presently, he is an Assistant Professor at
Michigan State University. His research interests include statistical
and nonlinear signal processing, image processing, and related
applications.

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