Gu Xuejun, Ren Kui, Masciotti James, Hielscher Andreas H
Dept. of Biomed. Eng., Columbia Univ., New York, NY 10027, USA.
Conf Proc IEEE Eng Med Biol Soc. 2006;2006:2667-70. doi: 10.1109/IEMBS.2006.260084.
Optical tomography consists of reconstructing the spatial of a medium's optical properties from measurements of transmitted light on the boundary of the medium. Mathematically this problem amounts to parameter identification for the radiative transport equation (ERT) or diffusion approximation (DA). However, this type of boundary-value problem is highly ill-posed and the image reconstruction process is often unstable and non-unique. To overcome this problem, we present a parametric inverse method that considerably reduces the number of variables being reconstructed. In this way the amount of measured data is equal or larger than the number of unknowns. Using synthetic data, we show examples that demonstrate how this approach leads to improvements in imaging quality.
光学层析成像包括根据介质边界上透射光的测量值来重建介质光学特性的空间分布。从数学角度来看，这个问题相当于求解辐射传输方程（ERT）或扩散近似（DA）的参数识别问题。然而，这类边值问题是高度不适定的，图像重建过程往往不稳定且不唯一。为了克服这个问题，我们提出了一种参数反演方法，该方法显著减少了待重建变量的数量。通过这种方式，测量数据的数量等于或大于未知数的数量。我们使用合成数据展示了一些示例，这些示例说明了这种方法如何提高成像质量。
