Compressed Sensing -- 2009 Moursund Lectures, Day 2

Terence Tao, 2006 Fields Medal Recipient
University of California, Los Angeles
Lecture two of a three part series


Abstract: Suppose one wants to recover an unknown signal x in Rn from a given vector Ax=b in Rm of linear measurements of the signal x. If the
number of measurements m is less than the degrees of freedom n of the signal, then the problem is underdetermined and the solution x is not unique.
However, if we also know that x is sparse or _compressible__with respect to some basis, then it is a remarkable fact that (given some assumptions on the
measurement matrix A) we can reconstruct x from the measurements b with high accuracy, and in some cases with perfect accuracy. Furthermore, the
algorithm for performing the reconstruction is computationally feasible. This observation underlies the newly developing field of _compressed sensing_.
In this talk we will discuss some of the mathematical foundations of this field.


The Moursund lecures are an annual lecture series in which the University of Oregon brings a distinguished mathematician to campus. The lecture series is named after Andrew Moursund, who was the Math department's head from 1939 to 1970, and are partly paid for by an endowment formed by Moursund's widow (Lulu Moursund) and son (David Moursund).