2011-08-11 – Seminar: Frederik Simons
11 August, 2011 (4pm), 5 Merrion Square, Dublin 2
Speaker: Frederik Simons of Princeton University
Title: Promoting Sparsity and Localization in Geophysical Inverse Problems.
Sometimes we don’t have enough information, sometimes we have too much and need to choose; sometimes our data present a highly incomplete picture of the truth, and sometimes there is so much redundancy and overdeterminacy that we need to cull it down somehow. In this tutorial I will discuss several ways by which novel mathematical tools have shed much light on problems of this nature. I will talk about the problem of reconstructing global sea level from sparse, uncertain, scattered indicators of local sea level (the solution derived from Monte-Carlo techniques in a Bayesian framework). I will introduce the design of flexible parameterizations to render inverse problems in geodesy and geomagnetics sparse (a solution given by linear combinations of spherical harmonics called Slepian functions). Lastly, I will discuss the nascence of sparsity-promoting algorithms in global seismology (under a new design that ports fast Cartesian wavelet transforms onto the sphere and combines least-squares data fitting with the minimization of l-1 norms). For each of these subtopics I will briefly highlight the key mathematical innovations and discuss the often widespread implications of the results.