Department of Mathematics Calendar
Mark Iwen, Michigan State University, Sparse Fourier Transforms, Generalizations, and Extensions
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Compressive sensing has generated tremendous amounts of interest since first being proposed by Emmanuel Candes, David Donoho, Terry Tao, and others roughly a decade ago. This mathematical framework has its origins in (i) the observation that traditional signal processing applications, such as MRI imaging problems, often deal with the acquisition of signals which are known a priori to be sparse in some basis, as well as (ii) the subsequent realization that this knowledge could in fact be used to help streamline the signal acquisition process in the first place (by only taking the bare minimum of signal measurements necessary in order to reconstruct the important basis coefficients only). The resulting mathematical theory has since led to dramatic reductions in measurement needs over traditional approaches in many situations where one would previously have reconstructed a fuller set of a given signal’s basis coefficients only to later discard most of them as insignificant.