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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