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An under-determined system of linear equation has infinitely many solutions (if it has a solution). But, if we have some prior knowledge saying that the solution vector is "sparse" enough, then under certain conditions there exists a unique solution. Moreover we can find the solution in polynomial time by solving a linear program. This is a celebrated result (by Candes and Tao) that has created a whole new area called "*Compressed sensing*". In this talk I will introduce the problem, and will prove a simple version of such reconstruction of sparse vectors from an under-determined system of linear equations.
(For everything that you want to know about compressed sensing, visit http://dsp.rice.edu/cs)
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