PDMM: A Novel Primal-Dual Majorization-Minimization Algorithm for Poisson Phase-Retrieval Problem

In this paper, we introduce a novel iterative algorithm for the problem of phase-retrieval where the measurements consist of only the magnitude of linear function of the unknown signal, and the noise in the measurements follow Poisson distribution. The proposed algorithm is based on the principle of...

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Vydáno v:IEEE transactions on signal processing Ročník 70; s. 1241 - 1255
Hlavní autoři: Fatima, Ghania, Li, Zongyu, Arora, Aakash, Babu, Prabhu
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Data models
Extraterrestrial measurements
Fenchel dual representation
Iterative algorithms
Iterative methods
Linear functions
Majorization-Minimization (MM)
Maximum likelihood estimation
Minimization
Noise measurement
Optimization
Phase measurement
Phase-retrieval
Poisson data model
Poisson distribution
Retrieval
Saddle points
Saddle-point problem
Signal processing algorithms
ISSN:1053-587X, 1941-0476
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Popis
Shrnutí:In this paper, we introduce a novel iterative algorithm for the problem of phase-retrieval where the measurements consist of only the magnitude of linear function of the unknown signal, and the noise in the measurements follow Poisson distribution. The proposed algorithm is based on the principle of majorization-minimization (MM); however, the application of MM here is very novel and distinct from the way MM has been usually used to solve optimization problems in the literature. More precisely, we reformulate the original minimization problem into a saddle point problem by invoking Fenchel dual representation of the <inline-formula><tex-math notation="LaTeX">\log (\cdot)</tex-math></inline-formula> term in the Poisson likelihood function. We then propose tighter surrogate functions over both primal and dual variables resulting in a double-loop MM algorithm, which we have named as Primal-Dual Majorization-Minimization (PDMM) algorithm. The iterative steps of the resulting algorithm are simple to implement and involve only computing matrix vector products. We also extend our algorithm to handle various <inline-formula><tex-math notation="LaTeX">\ell _{1}</tex-math></inline-formula> regularized Poisson phase-retrieval problems (which exploit sparsity). The proposed algorithm is compared with previously proposed algorithms such as wirtinger flow (WF), MM (conventional), and alternating direction methods of multipliers (ADMM) for the Poisson data model. The simulation results under different experimental settings show that PDMM is faster than the competing methods, and its performance in recovering the original signal is at par with the state-of-the-art algorithms.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2022.3156014