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Stable phase retrieval with low-redundancy frames · Around

2013

Stable phase retrieval with low-redundancy frames

Bodmann, Bernhard G., Hammen, Nathaniel

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We investigate the recovery of vectors from magnitudes of frame coefficients when the frames have a low redundancy, meaning a small number of frame vectors compared to the dimension of the Hilbert space.

We first show that for vectors in d dimensions, 4d-4 suitably chosen frame vectors are sufficient to uniquely determine each signal, up to an overall unimodular constant, from the magnitudes of its frame coefficients.
Then we discuss the effect of noise and show that 8d-4 frame vectors provide a stable recovery if part of the frame coefficients is bounded away from zero.
In this regime, perturbing the magnitudes of the frame coefficients by noise that is sufficiently small results in a recovery error that is at most proportional to the noise level.

Built on

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Then

B. G. Bodmann, P. G. Casazza, D. Edidin, R. Balan, Fast algorithms for signal reconstruction without phase, Proc. SPIE 6701, Wavelets XII (2007) 67011L
2007
Later among the works it cites.
O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, J. F. van der Veen, Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels, Acta Cryst. A63 (2007) 306–314
2007
Later among the works it cites.
R. Balan, B. G. Bodmann, P. G. Casazza, D. Edidin, Painless reconstruction from magnitudes of frame coefficients, J. Fourier Anal. Appl. 15 (2009) 488–501
2009
Later among the works it cites.

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