Imaging and Computing Seminar

Julius Kusuma, Schlumberger-Doll Research

A parametric approach to acquisition of signals with a finite rate of innovation: results and challenges

The science and engineering of sparse signal acquisition have gathered significant interest in recent years.  Both non-parametric and parametric approaches have been studied, promising novel ways to sample certain signals at rates well below the Nyquist rate.  In this talk we focus on the work of Vetterli et al. that showed it is possible to reconstruct parametrically described signals from samples taken at or near their innovation rate.  A majority of these approaches rely on the solution to a form of exponential fitting, for both real-valued and complex-valued cases.  Therefore, analysis and understanding of how algorithms for solving exponential fitting behave in the presence of noise is very important.

In this talk we will review some basic results, discuss the prospects in various application areas including novel signal acquisition technologies, and highlight what insights and features might be desirable to bring this theoretical idea to further practice.  Questions such as how to analyze and deal with undersampling/aliasing and how to build efficient devices are explored.