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Mark Iwen : Signal Recovery via Discrete Measurement Matrices

We will discuss a class of binary measurement matrices having a simple discrete incoherence property. These matrices can be shown to have both useful analytic (i.e., restricted isometry and l1-approximation properties) and combinatorial (i.e., group testing and expander graph related) structure which allows them to be utilized for sparse signal approximation in the spirit of compressive sensing. In addition, their structure allows the actual signal recovery process to be carried out by highly efficient algorithms once measurements have been taken. One application of these matrices and their related recovery algorithms is their application to the development of sublinear-time Fourier methods capable of accurately approximating periodic functions using far fewer samples and run time than required by standard Fourier transform techniques.

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