[PAST EVENT] CSUMS Lecture/Mathematics Colloquium: Louis Yang Liu (William & Mary)
November 11, 2011
2pm - 3pm
Abstract: Sparse or compressible signal or images can be recovered by solving the optimization problem of finding the solution with the smallest number of non-zero elements to an under-determined linear system, and one can use the lq-approach to solve the problem. In this talk, we'll explain that the null space property for the setting of the sparse solution vectors for multiple linear systems is equivalent to the null space property for the standard minimization in l_q-quasinorm subject to one linear system, that answers two open questions raised by Foucart and Gribonval. Another property which compressed sensing techniques rely on is the restricted isometry property of the sensing matrix. This property is related to the extremal singular values of the matrix, on which some probability estimates for the singular values of random matrices induced by lq-quasinorm can be obtained.