Seminars

From Sparse Interpolation to Compact Biomedical Signals: Prony Revisited

Dr. Wen-Shin Lee
Mathematics & Computer Science
Universiteit Antwerpen (CMI)

In Byron 516 at 14:00 on Friday January 28th


In 1795, Gaspard Riche de Prony developed a method that can extract a sum of exponentials from a set of equally spaced samples. While this method has been used to estimate the frequencies and amplitudes of a signal, numerical challenges exist in the implementations. Then in 1999, based on an interpretation as a shape reconstruction from moments, Prony’s method has been reformulated as a generalized eigenvalue problem, which can be viewed as a variant of structured total least squares in numerical linear algebra.

We depart from sparse polynomial interpolation in the (at first sight unrelated) field of computer algebra and explain an interesting connection to Prony’s method. Such connection enables symbolic-numeric sparse interpolation algorithms to be generated to a wider class of bases. We plan to discuss the corresponding issues in linear algebra and investigate applications in identifying compact representations of biomedical signals.Wen-Shin Lee

http://cant.ua.ac.be/members/wenshin.lee