Special topics course on Mathematical Introduction to Compressive Sensing, by Michael Lacey, offered Fall 2016.
A Mathematical Introduction to Compressive Sensing. Authors: Foucart, Simon, Rauhut, Holger (GaTech students can get an electronic copy from the library website. A free GT-network download)
Compressive sensing concerns the analysis of signals which are 'compressive' or 'sparse' in that they admit a description that is substantially smaller than their presentation. Topics to be covered include
Sparse solutions to under determined systems of equations
Basic algorithms, including ell^1 minimization
Tools of probability theory
Random methods in compressive sensing
Restricted Isometry Property
Will assume familiarity with linear algebra, and familiarity with probability theory, convex analysis and some statistical analysis will assumed from time to time.