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- W3003920102 abstract "We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with arbitrary off the grid nodes (equivalently, a rectangular Vandermonde matrix with the nodes on the unit circle) in the case when some of the nodes are separated by less than the inverse bandwidth. The bound is polynomial in the reciprocal of the so-called superresolution factor, while the exponent is controlled by the maximal number of nodes which are clustered together. As a corollary, we obtain sharp minimax bounds for the problem of sparse superresolution on a grid under the partial clustering assumptions." @default.
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- W3003920102 date "2020-01-01" @default.
- W3003920102 modified "2023-09-26" @default.
- W3003920102 title "Conditioning of Partial Nonuniform Fourier Matrices with Clustered Nodes" @default.
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- W3003920102 doi "https://doi.org/10.1137/18m1212197" @default.
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