Smoothed amplitude flow-based phase retrieval algorithm |
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| Institution: | 1. School of Computer and Information Engineering, Fuyang Normal University, Fuyang 236037, China;2. College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;3. College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China;1. College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, China;2. School of Information Science and Engineering, East China University of Science and Technology, Shanghai 200237, China;1. School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, China;2. College of Information Science and Technology, Donghua University, Shanghai, 201620, China;1. Faculty of Science, Yibin University, Yibin, Sichuan 644000, China;2. College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China;3. School of Mathematical and Statistics, Southwest University, Chongqing 400715, China;4. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China |
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| Abstract: | Phase retrieval recovers signals from linear phaseless measurements via minimizing a quadratic or amplitude function, while its loss function is generally either non-convex or non-smooth. Existing methods are used to add a truncation procedure or reweighting to the gradient during the gradient descent process to address the non-smooth problem. However, these methods often cause inconsistency in the search direction and increase the sampling complexity. This paperproposes a smoothed amplitude flow-based phase retrieval (SAFPR) algorithm to solve these problems. By introducing the smoothing function into the phase retrieval problem, the loss function is smoothed, significantly reducing the sampling complexity. Moreover, we also develop a stochastic smooth amplitude flow-based phase retrieval (SSAF) algorithm with practical, scalable, and fast in large-scale applications. Experimental results show that whether SAFPR or SSAF, the number of measurements required to reconstruct the signal entirely is better than the existing most advanced phase retrieval algorithms. The proposed methods also perform well in terms of time cost and convergence rate. |
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