Compressive Sensing with Applications to Fast Forward Modeling and Acoustic Source Localization

Abstract:

In the first part of this talk, we will give an overview of the recently developed theory of compressive sampling (CS), and discuss how this theory has influenced next-generation sensor design.  The CS paradigm can be summarized neatly: the number of measurements (e.g. samples) needed to acquire a signal or image depends more on its inherent information content than on the desired resolution (e.g. number of pixels).  The theory of CS is far-reaching and draws on subjects as varied as sampling theory, convex optimization, source and channel coding, statistical estimation, uncertainty principles, and harmonic analysis.  The applications of CS range from the familiar (imaging in medicine and radar, high-speed analog-to-digital conversion, and super-resolution) to truly novel image acquisition and encoding techniques.

In the second part of the talk, we will show how some of the key ideas of CS can be used to dramatically reduce the computation required for two types of forward modeling problems.  In the first, we show how all of the channels in a multiple-input multiple-output system can be acquired jointly by simultaneously exciting all of the inputs with different random waveforms, and give an immediate application to seismic forward modeling.  In the second, we consider the problem of acoustic source localization in a complicated channel.  We show that the amount of computation to perform "matched field processing" (matched filtering) can be reduced by precomputing the response of the channel to a small number of dense configurations of random sources.