摘要翻译：
提出了一种基于凸松弛的大规模一般相位恢复算法。一般的相位恢复问题包括I.A。根据记录在像（焦）平面上的点源的强度测量来估计光瞳平面内光场的相位。将寻找产生正确强度的复场的非凸问题转化为秩约束问题。利用核范数得到相位恢复问题的凸松弛。提出了一种新的迭代方法，即基于凸优化的相位恢复(COPR)，每次迭代由求解一个凸问题组成。在无噪声情况下，对于一类相位恢复问题，最小化问题的解线性收敛或更快地收敛到正确解。由于核范数极小化问题的解可以用半定规划计算，而这在可扩展性方面往往是一个昂贵的优化问题，我们提供了一个利用问题结构的快速ADMM算法。在一个实际的数值模拟研究中证明了COPR算法的性能，证明了它在可靠性和速度方面相对于现有方法的改进。
---
英文标题：
《Solving large-scale general phase retrieval problems via a sequence of
  convex relaxations》
---
作者：
Reinier Doelman and H. Thao Nguyen and Michel Verhaegen
---
最新提交年份：
2018
---
分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
--
一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
--

---
英文摘要：
  We present a convex relaxation-based algorithm for large-scale general phase retrieval problems. General phase retrieval problems include i.a. the estimation of the phase of the optical field in the pupil plane based on intensity measurements of a point source recorded in the image (focal) plane. The non-convex problem of finding the complex field that generates the correct intensity is reformulated into a rank constraint problem. The nuclear norm is used to obtain the convex relaxation of the phase retrieval problem. A new iterative method, indicated as Convex Optimization-based Phase Retrieval (COPR), is presented, with each iteration consisting of solving a convex problem. In the noise-free case and for a class of phase retrieval problems the solutions of the minimization problems converge linearly or faster towards a correct solution. Since the solutions to nuclear norm minimization problems can be computed using semidefinite programming, and this tends to be an expensive optimization in terms of scalability, we provide a fast ADMM algorithm that exploits the problem structure. The performance of the COPR algorithm is demonstrated in a realistic numerical simulation study, demonstrating its improvements in reliability and speed with respect to state-of-the-art methods.
---
PDF链接：
https://arxiv.org/pdf/1803.02652