Exact Phase Retrieval in Principal Shift-Invariant Spaces

Shenoy, Basty Ajay and Mulleti, Satish and Seelamantula, Chandra Sekhar (2016) Exact Phase Retrieval in Principal Shift-Invariant Spaces. In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, 64 (2). pp. 406-416.

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Abstract

We address the problem of phase retrieval from Fourier transform magnitude spectrum for continuous-time signals that lie in a shift-invariant space spanned by integer shifts of a generator kernel. The phase retrieval problem for such signals is formulated as one of reconstructing the combining coefficients in the shift-invariant basis expansion. We develop sufficient conditions on the coefficients and the bases to guarantee exact phase retrieval, by which we mean reconstruction up to a global phase factor. We present a new class of discrete-domain signals that are not necessarily minimum-phase, but allow for exact phase retrieval from their Fourier magnitude spectra. We also establish Hilbert transform relations between log-magnitude and phase spectra for this class of discrete signals. It turns out that the corresponding continuous-domain counterparts need not satisfy a Hilbert transform relation; notwithstanding, the continuous-domain signals can be reconstructed from their Fourier magnitude spectra. We validate the reconstruction guarantees through simulations for some important classes of signals such as bandlimited signals and piecewise-smooth signals. We also present an application of the proposed phase retrieval technique for artifact-free signal reconstruction in frequency-domain optical-coherence tomography (FDOCT).

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON SIGNAL PROCESSING
Publisher:	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Additional Information:	Copy right for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Keywords:	Phase retrieval; shift-invariant space; minimum-phase signals; Hilbert transform; frequency-domain optical-coherence tomography
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	28 Jan 2016 06:00
Last Modified:	28 Jan 2016 06:00
URI:	http://eprints.iisc.ac.in/id/eprint/53167

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