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Local and global phaseless sampling in real spline spaces. (English) Zbl 1465.94025

Summary: We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on the whole line from infinitely many unsigned samples. In both cases, we give characterizations for a set of points to be a phaseless sampling set, at which any nonseparable function is determined up to a sign on an interval or on the whole line by its unsigned sampled values. Moreover, for the case of local recovery, we also study the almost phaseless sampling and give a necessary and sufficient condition for a set of points to admit a local recovery for almost all functions.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
94A20 Sampling theory in information and communication theory
41A15 Spline approximation
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Software:

BlockPR; SparsePR
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Full Text: DOI arXiv

References:

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[45] \endbiblist
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