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Nonuniform Generalized Sampling

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In this talk, we present a new extension of the method known as Generalized Sampling introduced by Anders Hansen and Ben Adcock. This new framework enables a stable and quasi-optimal reconstruction of a function in a separable Hilbert space from its non-uniformly distributed Fourier samples. The case when the Fourier samples are distributed non-uniformly is particularly challenging because the famous Nyquist—Shannon Sampling Theorem does not hold. We conclude with some thoughts on current research regarding the reconstruction in dimensions higher than one, which is important in applications to MRI , for example, when the samples are acquired along a spiral.

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

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