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Center for Nonlinear Studies |
The framework of Compressive Sensing (CS) is concerned with the recovery of an unknown sparse signal from an underdetermined system of linear equations. CS builds upon the fundamental fact that many signals can be represented using only a few non-zero coefficients in a suitable basis or dictionary. In CS framework, a small collection of linear random projections of such sparse signals contains sufficient information for reliable signal recovery. CS measurement scheme is universal in the sense that the same mechanism in acquiring measurements can be used irrespective of the sparsity level of the signal or the basis in which the signal is sparse. Although most of the CS literature has focused on complete recovery of sparse signals, there are several signal processing applications where complete signal recovery is not necessary. Very often, we are interested in solving inference problems where it is only necessary to extract certain information from compressive measurements. For example, in applications such as subset selection in linear regression, and spectrum sensing in cognitive radio networks, it is sufficient to estimate only the locations of non-zero elements (or the sparsity pattern) of the sparse signal. This talk will give an overview of Compressive Sensing and will discuss the problem of performing several inference tasks directly in the compressive measurement domain without first resorting to a full-scale signal reconstruction.
Host: Amy Galbraith, amyg@lanl.gov, 667-9108