论文标题
估计和使用反问题中的信息
Estimating and using information in inverse problems
论文作者
论文摘要
在反问题中,一种尝试从系统的间接测量中推断出空间可变函数。对于反问题的从业者来说,在讨论关键问题时,“信息”的概念是熟悉的,例如可以准确地推断出功能的哪些部分,哪些部分不能。例如,通常可以理解,我们只能准确地识别系统参数仅接近探测器,或沿源和检测器之间的射线路径,因为我们对这些位置有“最多的信息”。尽管在许多出版物中被引用,但在这种情况下被调用的“信息”并不是一个很好的理解和明确定义的数量。 本文中,我们介绍了信息密度的定义,该定义基于贝叶斯重新印度的逆问题重新印象的系数差异。然后,我们讨论了三个领域,其中此信息密度可以在解决方案解决方案的实际算法中有用,并说明了这些领域之一的有用性 - 如何使用数值实验选择重建函数的离散网格。
In inverse problems, one attempts to infer spatially variable functions from indirect measurements of a system. To practitioners of inverse problems, the concept of "information" is familiar when discussing key questions such as which parts of the function can be inferred accurately and which cannot. For example, it is generally understood that we can identify system parameters accurately only close to detectors, or along ray paths between sources and detectors, because we have "the most information" for these places. Although referenced in many publications, the "information" that is invoked in such contexts is not a well understood and clearly defined quantity. Herein, we present a definition of information density that is based on the variance of coefficients as derived from a Bayesian reformulation of the inverse problem. We then discuss three areas in which this information density can be useful in practical algorithms for the solution of inverse problems, and illustrate the usefulness in one of these areas -- how to choose the discretization mesh for the function to be reconstructed -- using numerical experiments.