TY - JOUR

T1 - STABILITY OF UNIQUE FOURIER-TRANSFORM PHASE RECONSTRUCTION.

AU - Sanz, Jorge L.C.

AU - Huang, Thomas S.

AU - Cukierman, Fernando

PY - 1983

Y1 - 1983

N2 - 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.

AB - 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.

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U2 - 10.1364/JOSA.73.001442

DO - 10.1364/JOSA.73.001442

M3 - Article

AN - SCOPUS:0020843950

SN - 0030-3941

VL - 73

SP - 1442

EP - 1445

JO - Journal of the Optical Society of America

JF - Journal of the Optical Society of America

IS - 11

ER -