Inverse problems with Poisson data (C09)

泊松数据的反演问题 (C09)

• 批准号: 199872343
• 金额: --
• 依托单位: Institut für Numerische und Angewandte Mathematik (NAM)
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/199872343?language=en
• 关键词: Inverse; problems; Poisson; data; C09

This project is devoted to regularization theory and algorithms for inverse problems with Poisson distributed data. As typical for photonic imaging applications, data are described by a vector of independent Poisson distributed random variables, or in the continuous case by a Poisson point process. We aim to prove optimal rates of convergence as the expected number of detected photons tends to infinity in some relevant open cases. Moreover, we study new Newton-type regularization methods tailored Kullback-Leibler data fidelity terms. The inversion methods developed in this project will be used for the joint reconstruction of object and phase in isoSTED microscopy and phase retrieval problems in x-ray microscopy.

该项目致力于泊松分布数据的逆问题的正则化理论和算法。作为光子成像应用的典型特征，数据由独立泊松分布式变量的向量描述，或者在连续情况下通过泊松点过程描述。我们的目标是证明收敛的最佳速率，因为在某些相关的开放式案例中，检测到的光子的预期数量倾向于无穷大。此外，我们研究了新的牛顿型正则化方法量身定制的Kullback-Leibler数据保真度。该项目中开发的反转方法将用于在X射线显微镜中的等静力显微镜和相位检索问题中的对象和相位的联合重建。