标题： 成像系统中的反问题和一般的贝叶斯反演框架 显示英文标题

标题： Inverse problems in imaging systems and the general Bayesian inversion frawework

摘要： 在本文中，首先介绍了在仪器、计算机成像系统和计算机视觉中出现的大量反问题。 然后给出了它们的通用正向模型，并提出了相应的反问题。 接着，在展示了经典解析方法和最小二乘法对于这些不适定反问题的不足之后，提出了一种贝叶斯估计框架，该框架可以以一致的方式处理所有这些问题。 贝叶斯反演框架中的一个重要步骤是对未知量进行先验建模。 因此，介绍了大量的此类模型，特别是复合隐马尔可夫模型。 然后简要介绍了贝叶斯估计的主要计算工具。 最后，详细研究了一些特殊情况，并提出了新的结果。 显示英文摘要

摘要： In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Bayesian estimation framework is presented which can handle, in a coherent way, all these problems. One of the main steps, in Bayesian inversion framework is the prior modeling of the unknowns. For this reason, a great number of such models and in particular the compound hidden Markov models are presented. Then, the main computational tools of the Bayesian estimation are briefly presented. Finally, some particular cases are studied in detail and new results are presented.