Regularization of the factorization method applied to diffuse optical tomography
Regularization of the factorization method applied to diffuse optical tomography
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DOI：
10.1088/1361-6420/ac37f9
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发表时间：
2021-06
期刊：
影响因子：
2.1
通讯作者：
I. Harris
中科院分区：
文献类型：
--
作者：
I. Harris
在本文中，我们开发了一种新的正则化版本的分解方法，用于将复杂的希尔伯特空间映射到对偶空间。因式分解方法使用皮卡德准则来定义指示函数来对未知区域进行成像。在大多数应用中，数据运算符是紧凑的，这使得奇异值可以快速趋于零，这可能导致数值不稳定。这里提出的因式分解方法的正则化旨在避免应用皮卡德准则时的数值不稳定。这种方法允许人们以一种计算简单且分析严格的方式在几乎没有先验信息的情况下对物体的内部结构进行成像。在这里，我们将重点关注该方法在漫射光学断层扫描中的应用，其中将证明该方法可用于从狄利克雷到诺依曼映射中恢复未知的子区域。数值示例将以二维形式呈现。
In this paper, we develop a new regularized version of the factorization method for positive operators mapping a complex Hilbert space into it is dual space. The factorization method uses Picard’s criteria to define an indicator function to image an unknown region. In most applications the data operator is compact which gives that the singular values can tend to zero rapidly which can cause numerical instabilities. The regularization of the factorization method presented here seeks to avoid the numerical instabilities in applying Picard’s criteria. This method allows one to image the interior structure of an object with little a priori information in a computationally simple and analytically rigorous way. Here we will focus on an application of this method to diffuse optical tomography where will prove that this method can be used to recover an unknown subregion from the Dirichlet-to-Neumann mapping. Numerical examples will be presented in two dimensions.