Exact Phase Retrieval for a Class of 2-D Parametric Signals

Shenoy, Basty Ajay and Seelamantula, Chandra Sekhar (2015) Exact Phase Retrieval for a Class of 2-D Parametric Signals. In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, 63 (1). pp. 90-103.

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Abstract

We address the problem of two-dimensional (2-D) phase retrieval from magnitude of the Fourier spectrum. We consider 2-D signals that are characterized by first-order difference equations, which have a parametric representation in the Fourier domain. We show that, under appropriate stability conditions, such signals can be reconstructed uniquely from the Fourier transform magnitude. We formulate the phase retrieval problem as one of computing the parameters that uniquely determine the signal. We show that the problem can be solved by employing the annihilating filter method, particularly for the case when the parameters are distinct. For the more general case of the repeating parameters, the annihilating filter method is not applicable. We circumvent the problem by employing the algebraically coupled matrix pencil (ACMP) method. In the noiseless measurement setup, exact phase retrieval is possible. We also establish a link between the proposed analysis and 2-D cepstrum. In the noisy case, we derive Cramer-Rao lower bounds (CRLBs) on the estimates of the parameters and present Monte Carlo performance analysis as a function of the noise level. Comparisons with state-of-the-art techniques in terms of signal reconstruction accuracy show that the proposed technique outperforms the Fienup and relaxed averaged alternating reflections (RAAR) algorithms in the presence of noise.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON SIGNAL PROCESSING
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copyright for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Keywords:	Algebraically coupled matrix pencil method; annihilating filter; finite rate of innovation; phase retrieval
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	28 Jan 2015 04:20
Last Modified:	28 Jan 2015 04:20
URI:	http://eprints.iisc.ac.in/id/eprint/50743

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