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20102026
most citedOn instabilities of deep learning in image reconstruction - Does AI come at a cost?

795 citations · 1.3k across the 32 of their papers we have counts for

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math.NA2010

Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon

Ben Adcock, Anders C. Hansen

We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number…

math.NA2010★ 4 cited

A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases

Ben Adcock, Anders C. Hansen

We introduce a generalized framework for sampling and reconstruction in separable Hilbert spaces. Specifically, we establish that it is always possible to stably reconstruct a vect…