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A nonlinear approach to generalized sampling

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One of the central problems of sampling theory is the reconstruction of an image or a signal from a collection of measurements. Typically, this problem may be modeled in a Hilbert space setting and measurements are taken with respect to some set of vectors, such as some Fourier basis. Generalized sampling is a framework for obtaining reconstructions in arbitrary spaces without constraints on the type of measurements. In my talk, I will present generalized sampling as an l^1 minimization problem and apply this framework to the reconstruction of wavelets coefficients from Fourier samples. I will also briefly discuss some implications of generalized sampling for the use of variable density sampling schemes in compressed sensing.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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