STABILITY OF UNIQUE FOURIER-TRANSFORM PHASE RECONSTRUCTION.

Jorge L.C. Sanz, Thomas S. Huang, Fernando Cukierman

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of Fourier-transform phase reconstruction from the Fourier-transform magnitude of multidimensional discrete signals is considered. It is well known that, if a discrete finite-extent n-dimensional signal (n greater than equivalent to 2) has an irreducible z transform, then the signal is uniquely determined from the magnitude of its Fourier transform. It is also known that this irreducibility condition holds for all multidimensional signals except for a set of signals that has measure zero. It is shown that this uniqueness condition is stable in the sense that it is not sensitive to noise. Specifically, it is proved that the set of signals whose z transform is reducible is contained in the zero set of a certain multidimensional polynomial. Several important conclusions can be drawn from this characterization, and, in particular, the zero-measure property is obtained as a simple byproduct.

Original languageEnglish (US)
Pages (from-to)1442-1445
Number of pages4
JournalJournal of the Optical Society of America
Volume73
Issue number11
DOIs
StatePublished - Jan 1 1983

ASJC Scopus subject areas

  • Engineering(all)

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