Phase Retrieval From Binary Measurements

Mukherjee, Subhadip and Seelamantula, Chandra Sekhar (2018) Phase Retrieval From Binary Measurements. In: IEEE SIGNAL PROCESSING LETTERS, 25 (3). pp. 348-352.

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Abstract

We consider the problem of signal reconstruction from quadratic measurements that are encoded as +1 or -1 depending on whether they exceed a predetermined positive threshold or not. Binary measurements are fast to acquire and inexpensive in terms of hardware. We formulate the problem of signal reconstruction using a consistency criterion, wherein one seeks to find a signal that is in agreement with the acquired measurements. To enforce consistency, we construct a convex cost using a one-sided quadratic penalty and minimize it using an iterative accelerated projected gradient-descent technique. The projected gradient-descent (PGD) scheme reduces the cost function in each iteration, whereas incorporating momentum into PGD, notwithstanding the lack of such a descent property, exhibits faster convergence than PGD empirically. We refer to the resulting algorithm as binary phase retrieval (BPR). Considering additive white noise contamination prior to quantization, we also derive the Cramer-Rao Bound (CRB) for the binary encoding model. Experimental results demonstrate that the BPR algorithm yields a signal-to-reconstruction error ratio (SRER) of approximately 25 dB in the absence of noise. In the presence of noise prior to quantization, the SRER is within 2 to 3 dB of the CRB.

Item Type:	Journal Article
Publication:	IEEE SIGNAL PROCESSING LETTERS
Additional Information:	Copy right for this article belong to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	02 Mar 2018 14:57
Last Modified:	02 Mar 2018 14:57
URI:	http://eprints.iisc.ac.in/id/eprint/59036

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