Mathematical and numerical challenges in optical screening of female breast
Mathematical and numerical challenges in optical screening of female breast
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DOI：
10.1002/cnm.3286
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发表时间：
2019-12-23
影响因子：
2.1
通讯作者：
Weishaeupl, Rada-M.
中科院分区：
文献类型：
--
作者：
Causin, Paola;Lupieri, Marina G.;Weishaeupl, Rada-M.
漫反射光学层析成像(DOT)是一种新兴的成像技术，它以非侵入性和非电离的方式利用光进行诊断。在本文中，我们重点研究了斑点技术在女性乳房筛查中的应用，即通过光源照射乳房表面，并将出射光收集到乳房表面。测量的光数据与从相关数学模型获得的等效场的比较产生了DOT逆问题，其解提供了组织的光学系数的估计。而后者又与癌症检测的临床标记物有关。这项工作的目标是提出一种适合于DOT成像设备的概念的数学和计算方法，该设备能够以负担得起的成本进行快速和准确的筛查。也就是说，我们解决了关于严重病态DOT反问题的解的关键问题的两个原点：(A)基于格林函数的计算方法，它不需要组织几何的精确知识，这里在基本解方法的下降中提出了允许强制正确边界条件的计算方法；(B)弹性网正则化技术，它具有L(2)和L(1)-范数惩罚方法的理想性质，并为光学系数场和精化过程中的稀疏性识别打开了可能性。
Diffuse optical tomography (DOT) is an emerging imaging technique which uses light for diagnostic purposes in a non-invasive and non-ionizing way. In this paper, we focus on DOT application to female breast screening, where the surface of the breast is illuminated by light sources and the outgoing light is collected on the surface. The comparison of measured light data with the equivalent field obtained from a relevant mathematical model yields the DOT inverse problem whose solution provides an estimate of the optical coefficients of the tissue. These latter, in turn, can be related to clinical markers for cancer detection. The goal of this work is to propose a mathematical and computational approach tailored to the concept of a DOT imaging device able to perform fast and accurate screenings at an affordable cost. Namely, we address two original points about the crucial issue of the solution of the severely ill-conditioned DOT inverse problem: (a) a computational approach based on Green's functions which do not require the exact knowledge of the tissue geometry, proposed here in the declination of the Method of Fundamental Solutions, which allows to enforce correct boundary conditions; (b) the elastic net regularization technique that shares the desirable properties of both the l(2)- and l(1)-norm penalization approaches and opens the possibility for sparsity recognition in the optical coefficients field and refinement procedures.