Tuesday, November 19, 1996
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.
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.