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tao2

Lecture 2: Compressed Sensing
4:00 p.m., Wednesday, 11 November 2009 – 221 McKenzie

Abstract: Suppose one wants to recover an unknown signal x in R^n from a given vector Ax=b in R^m 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.