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	On Gradient Descent Algorithm for Generalized Phase Retrieval Problem
	Ji, Li ; Tie, Zhou
	2016
关键词	phase retrieval gradient descent global convergence LBFGS local convexity OPTIMIZATION
英文摘要	In this paper, we study the generalized phase retrieval problem: to recover a signal x is an element of C-n from the measurements y(r) = vertical bar < ar, x >vertical bar(2), r = 1, 2, . . . , m. The problem can be reformulated as a least-squares minimization problem. Although the cost function is nonconvex, the global convergence of gradient descent algorithm from a random initialization is studied, when m is large enough. We improve the known result of the local convergence from a spectral initialization. When the signal x is real-valued, we prove that the cost function is local convex near the solution { +/- x }. To accelerate the gradient descent, we apply several efficient line search methods. We also perform a comparative numerical study of the line search methods and the alternative projection method. Numerical simulations demonstrate the superior ability of LBFGS algorithm than other algorithms.; NSF of China [61421062, 11471024]; CPCI-S(ISTP); 320-325
语种	英语
出处	SCI
出版者	13th IEEE International Conference on Signal Processing (ICSP)
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/470071]
专题	数学科学学院
推荐引用方式 GB/T 7714	Ji, Li,Tie, Zhou. On Gradient Descent Algorithm for Generalized Phase Retrieval Problem. 2016-01-01.

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