Convex Augmentation for Total Variation Based Phase Retrieval
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Abstract (arXiv)
Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a convex augmentation approach for phase retrieval based on total variation regularization. In contrast to popular convex relaxation models like PhaseLift, our model can be efficiently solved by a modified semi-proximal alternating direction method of multipliers (sPADMM). The modified sPADMM is more general and flexible than the standard one, and its convergence is also established in this paper. Extensive numerical experiments are conducted to showcase the effectiveness of the proposed method.
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References · 8
- 2014Phase Retrieval via Wirtinger Flow: Theory and Algorithmscited by 123
- 2015Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systemscited by 50
- 2016Solving Systems of Random Quadratic Equations via Truncated Amplitude Flowcited by 28
- 2013Phase Retrieval from Coded Diffraction Patternscited by 26
- 2013Sparse Phase Retrieval: Convex Algorithms and Limitationscited by 7
- 2016Reshaped Wirtinger Flow and Incremental Algorithm for Solving Quadratic System of Equationscited by 4
- 2016Phase Retrieval from 1D Fourier Measurements: Convexity, Uniqueness, and Algorithmscited by 3
- 2014A Convergent 3-Block Semi-Proximal ADMM for Convex Minimization Problems with One Strongly Convex Blockcited by 2
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