Locating small inclusions in diffuse optical tomography by a direct imaging method

Abstract

Abstract 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.