Optical tomography is a typical non-invasive medical imaging technique, which aims to reconstruct geometric and physical properties of tissues by passing near infrared light through tissues for obtaining the intensity measurements. Other than optical properties of tissues, we are interested in finding locations of small inclusions inside the object from boundary measurements, based on the time-dependent diffusion model. First, we analyze the asymptotic behavior of the boundary measurements weighted by the fundamental solution of a backward diffusion equation as the diameters of inclusions go to zero. Then, we derive an efficient algorithm for locating small inclusions by finite boundary measurements. This algorithm is direct, simple and easy to be implemented numerically, since it only involves matrix operations and has no iteration process. Finally, some numerical results are presented to illustrate the feasibility and robustness of the algorithm. A new observation of the algorithm is that we can take the source points and test points independently and increase the resolution of numerical results by taking more test points.

中文翻译：

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通过直接成像方法在漫射光学层析成像中定位小夹杂物

光学层析成像是一种典型的非侵入性医学成像技术，旨在通过使近红外光穿过组织以获得强度测量值来重建组织的几何和物理特性。除了组织的光学特性，我们还有兴趣根据时间相关的扩散模型从边界测量中找到物体内部小夹杂物的位置。首先，当夹杂物的直径变为零时，我们分析了由向后扩散方程的基本解加权的边界测量值的渐近行为。然后，我们导出了一种通过有限边界测量来定位小夹杂物的有效算法。该算法直接，简单且易于在数值上实现，因为它只涉及矩阵运算，没有迭代过程。最后，给出了一些数值结果，说明了该算法的可行性和鲁棒性。该算法的一个新发现是，我们可以独立获取源点和测试点，并通过获取更多测试点来提高数值结果的分辨率。