Mathematics Colloquium

Thursday, January 25, 1996, 4:00pm

102 Bradley Hall

Professor Bernard Mair

University of Florida (visiting Dartmouth)

speaks on

A Unified Theory for Statistical and Deterministic Inverse Problems

Abstract. The problem of estimating a signal from indirect measurements (usually given in terms of a low pass filter), and blurred by random noise is considered a determinstic inverse problem. Non-parametric, (possibly indirect) density and regression estimation, are examples of what we consider statistical inverse problems. Traditionally, these problems have been investigated by researchers in different areas. Usually regression involves compact operators and density estimation (e.g. deconvolution) may involve noncompact operators. Systematic accounts in the statistical literature are mostly restricted to compact operators, and the noncompact cases are often dealt with in an adhoc manner. This talk will describe a unified method, based on regularized operator inversion, to deal with signal recovery in both deterministic and statistical inverse problems.

To apply this method, it is crucial to determine the appropriate ``degree of regularization''. While this can be obtained from apriori knowledge of the unknown signal, this information is often not available. If time allows, we will also discuss purely data-based methods of determining the appropriate degree of regularization.

Tea. High tea will be served at 3:30pm in the Lounge.
Emmy's. Certain refreshments will be available at the Emmy's after the talk.