Conditioning of Partial Nonuniform Fourier Matrices with Clustered Nodes
Name
18m1212197.pdf
Description
Published version
Size
849.26 KB
Format
Adobe PDF
Checksum (MD5)
8564fa0ea09ae7b404d94ac75788b9e5
Author(s)
Batenkov, Dmitry
Demanet, Laurent
Goldman, Gil
Yomdin, Yosef
Date Issued
2020
Journal
SIAM Journal on Matrix Analysis and Applications
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
© 2020 Society for Industrial and Applied Mathematics 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1137/18M1212197
