Hielscher A H, Bartel S
Department of Pathology, State University of New York, Downstate Medical Center, 450 Clarkson Avenue, Box 25, Brooklyn, New York 11203, USA.
J Biomed Opt. 2001 Apr;6(2):183-92. doi: 10.1117/1.1352753.
It is well known that the reconstruction problem in optical tomography is ill-posed. In other words, many different spatial distributions of optical properties inside the medium can lead to the same detector readings on the surface of the medium under consideration. Therefore, the choice of an appropriate method to overcome this problem is of crucial importance for any successful optical tomographic image reconstruction algorithm. In this work we approach the problem within a gradient-based iterative image reconstruction scheme. The image reconstruction is considered to be a minimization of an appropriately defined objective function. The objective function can be separated into a least-square-error term, which compares predicted and actual detector readings, and additional penalty terms that may contain a priori information about the system. For the efficient minimization of this objective function the gradient with respect to the spatial distribution of optical properties is calculated. Besides presenting the underlying concepts in our approach to overcome ill-posedness in optical tomography, we will show numerical results that demonstrate how prior knowledge, represented as penalty terms, can improve the reconstruction results.
众所周知，光学层析成像中的重建问题是不适定的。换句话说，介质内部许多不同的光学特性空间分布可能导致在所考虑的介质表面上产生相同的探测器读数。因此，选择一种合适的方法来克服这个问题对于任何成功的光学层析成像图像重建算法都至关重要。在这项工作中，我们在基于梯度的迭代图像重建方案中处理这个问题。图像重建被认为是对一个适当定义的目标函数进行最小化。目标函数可以分为一个最小二乘误差项，它比较预测的和实际的探测器读数，以及可能包含关于系统的先验信息的附加惩罚项。为了有效地最小化这个目标函数，计算了相对于光学特性空间分布的梯度。除了介绍我们在克服光学层析成像不适定性方法中的基本概念外，我们还将展示数值结果，这些结果表明作为惩罚项表示的先验知识如何能够改善重建结果。
