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Phase Retrieval Algorithm via Nonconvex Minimization Using a Smoothing Function.
- Source :
-
IEEE Transactions on Signal Processing . 9/1/2018, Vol. 66 Issue 17, p4574-4584. 11p. - Publication Year :
- 2018
-
Abstract
- Phase retrieval is an inverse problem which consists in recovering an unknown signal from a set of absolute squared projections. Recently, gradient descent algorithms have been developed to solve this problem. However, their optimization cost functions are non-convex and non-smooth. To address the non-smoothness of the cost function, some of these methods use truncation thresholds to calculate a truncated step gradient direction. But, the truncation requires designing parameters to obtain a desired performance in the phase recovery, which drastically modifies the search direction update, increasing the sampling complexity. Therefore, this paper develops the Phase Retrieval Smoothing Conjugate Gradient method (PR-SCG) which uses a smoothing function to retrieve the signal. PR-SCG is based on the smooth-ing projected gradient method which is useful for non-convex optimization problems. PR-SCG uses a nonlinear conjugate gradient of the smoothing function as the search direction to accelerate the convergence. Furthermore, the incremental Stochastic Smoothing Phase Retrieval algorithm (SSPR) is developed. SSPR involves a single equation per iteration which results in a simple, scalable, and fast approach useful when the size of the signal is large. Also, it is shown that SSPR converges linearly to the true signal, up to a global unimodular constant. Additionally, the proposed methods do not require truncation parameters. Simulation results are provided to validate the efficiency of PR-SCG and SSPR compared to existing phase retrieval algorithms. It is shown that PR-SCG and SSPR are able to reduce the number of measurements and iterations to recover the phase, compared with recently developed algorithms. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1053587X
- Volume :
- 66
- Issue :
- 17
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Signal Processing
- Publication Type :
- Academic Journal
- Accession number :
- 132683916
- Full Text :
- https://doi.org/10.1109/TSP.2018.2855667