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	On Gradient Descent Algorithm for Generalized Phase Retrieval Problem; On Gradient Descent Algorithm for Generalized Phase Retrieval Problem
	Li Ji ; Zhou Tie
	2016
关键词	phase retrieval gradient descent global convergence LBFGS local convexity phase retrieval gradient descent global convergence LBFGS local convexity
英文摘要	In this paper,we study the generalized phase retrieval problem:to recover a signal x ∈ C~n from the measurements y_r = |〈a_r,x〉|~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.; In this paper,we study the generalized phase retrieval problem:to recover a signal x ∈ C~n from the measurements y_r = |〈a_r,x〉|~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; IEEE Beijing Section、IET Beijing Local Network、Beijing Jiaotong University; 6
语种	英语
出处	知网
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/479729]
专题	数学科学学院
推荐引用方式 GB/T 7714	Li Ji,Zhou Tie. On Gradient Descent Algorithm for Generalized Phase Retrieval Problem, On Gradient Descent Algorithm for Generalized Phase Retrieval Problem. 2016-01-01.

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