June 2018
Spotlight Summary by David Paganin
Constrained phase retrieval: when alternating projection meets regularization
Alternating-projection methods for phase retrieval take another step forward in this new paper by Shi and colleagues. This advance is achieved via a blending of the alternating-projection method for phase retrieval with a regularization model. This blend balances two factors, namely the fact that the reconstruction should be consistent with the data, while also being regulated by other desirable properties. This paper by Shi and colleagues is the latest in a long series of developments for the phase-retrieval concept, which date back at least as far as Wolfgang Pauli's famous question from 1933 as to whether a complex wave function can be reconstructed given its modulus in both real space and Fourier space. Many iterative approaches to this and related phase-retrieval problems stand on the shoulders of the alternating-projection method pioneered by Gerchberg and Saxton in 1972, in a paper whose lasting influence on the phase-retrieval literature remains as strong as ever. I warmly recommend this latest advance in phase retrieval to your attention.
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Article Information
Constrained phase retrieval: when alternating projection meets regularization
Baoshun Shi, Qiusheng Lian, Xin Huang, and Ni An
J. Opt. Soc. Am. B 35(6) 1271-1281 (2018) View: Abstract | HTML | PDF