TY - GEN
T1 - Compressive phase retrieval via generalized approximate message passing
AU - Schniter, Philip
AU - Rangan, Sundeep
PY - 2012
Y1 - 2012
N2 - In this paper, we propose a novel approach to compressive phase retrieval based on loopy belief propagation and, in particular, on the generalized approximate message passing (GAMP) algorithm. Numerical results show that the proposed PR-GAMP algorithm has excellent phase-transition behavior, noise robustness, and runtime. In particular, for successful recovery of synthetic Bernoulli-circular-Gaussian signals, PR-GAMP requires ≈4 times the number of measurements as a phase-oracle version of GAMP and, at moderate to large SNR, the NMSE of PR-GAMP is only ≈3 dB worse than that of phase-oracle GAMP. A comparison to the recently proposed convex-relation approach known as 'CPRL' reveals PR-GAMP's superior phase transition and orders-of-magnitude faster runtimes, especially as the problem dimensions increase. When applied to the recovery of a 65k-pixel grayscale image from 32k randomly masked magnitude measurements, numerical results show a median PR-GAMP runtime of only 13.4 seconds.
AB - In this paper, we propose a novel approach to compressive phase retrieval based on loopy belief propagation and, in particular, on the generalized approximate message passing (GAMP) algorithm. Numerical results show that the proposed PR-GAMP algorithm has excellent phase-transition behavior, noise robustness, and runtime. In particular, for successful recovery of synthetic Bernoulli-circular-Gaussian signals, PR-GAMP requires ≈4 times the number of measurements as a phase-oracle version of GAMP and, at moderate to large SNR, the NMSE of PR-GAMP is only ≈3 dB worse than that of phase-oracle GAMP. A comparison to the recently proposed convex-relation approach known as 'CPRL' reveals PR-GAMP's superior phase transition and orders-of-magnitude faster runtimes, especially as the problem dimensions increase. When applied to the recovery of a 65k-pixel grayscale image from 32k randomly masked magnitude measurements, numerical results show a median PR-GAMP runtime of only 13.4 seconds.
UR - http://www.scopus.com/inward/record.url?scp=84875716638&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84875716638&partnerID=8YFLogxK
U2 - 10.1109/Allerton.2012.6483302
DO - 10.1109/Allerton.2012.6483302
M3 - Conference contribution
AN - SCOPUS:84875716638
SN - 9781467345385
T3 - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
SP - 815
EP - 822
BT - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
T2 - 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
Y2 - 1 October 2012 through 5 October 2012
ER -