摘要翻译：
利用基于点扩展函数(PSF)工程的方法，研究了从二维数据恢复三维点源图像的高分辨率成像问题。该方法涉及到S.~Prasad最近提出的一项新技术，该技术基于使用具有单瓣的旋转PSF从散焦中获得深度。PSF的旋转量编码点源的深度位置。应用包括高分辨率单分子定位显微镜，以及本文所述的利用天基望远镜定位空间碎片的问题。将定位问题离散在一个立方格上，其中非零项的坐标表示点源的三维位置，这些项的值表示点源的通量。寻找点源的位置和通量是一个大规模的稀疏三维反问题。针对泊松噪声模型，提出了一种基于Kullback-Leibler(KL)散度的非凸正则化三维定位方法。此外，我们提出了一个新的方案估计源通量由KL数据拟合项。数值实验证明了算法的有效性和稳定性，这些算法是在随机的图像数据子集上训练的，然后再应用于其他图像。我们的三维定位算法也可以很好地应用于其他类型的深度编码PSFs。
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英文标题：
《Non-convex optimization for 3D point source localization using a
  rotating point spread function》
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作者：
Chao Wang, Raymond Chan, Mila Nikolova, Robert Plemmons, Sudhakar
  Prasad
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最新提交年份：
2018
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分类信息：

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。
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英文摘要：
  We consider the high-resolution imaging problem of 3D point source image recovery from 2D data using a method based on point spread function (PSF) engineering. The method involves a new technique, recently proposed by S.~Prasad, based on the use of a rotating PSF with a single lobe to obtain depth from defocus. The amount of rotation of the PSF encodes the depth position of the point source. Applications include high-resolution single molecule localization microscopy as well as the problem addressed in this paper on localization of space debris using a space-based telescope. The localization problem is discretized on a cubical lattice where the coordinates of nonzero entries represent the 3D locations and the values of these entries the fluxes of the point sources. Finding the locations and fluxes of the point sources is a large-scale sparse 3D inverse problem. A new nonconvex regularization method with a data-fitting term based on Kullback-Leibler (KL) divergence is proposed for 3D localization for the Poisson noise model. In addition, we propose a new scheme of estimation of the source fluxes from the KL data-fitting term. Numerical experiments illustrate the efficiency and stability of the algorithms that are trained on a random subset of image data before being applied to other images. Our 3D localization algorithms can be readily applied to other kinds of depth-encoding PSFs as well.
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PDF链接：
https://arxiv.org/pdf/1804.04