Kilmer Misha E, Miller Eric L, Barbaro Alethea, Boas David
Department of Mathematics, Tufts University, Medford, Massachusetts 02155, USA.
Appl Opt. 2003 Jun 1;42(16):3129-44. doi: 10.1364/ao.42.003129.
We present a shape-based approach to three-dimensional image reconstruction from diffuse optical data. Our approach differs from others in the literature in that we jointly reconstruct object and background characterization and localization simultaneously, rather than sequentially process for optical properties and postprocess for edges. The key to the efficiency and robustness of our algorithm is in the model we propose for the optical properties of the background and anomaly: We use a low-order parameterization of the background and another for the interior of the anomaly, and we use an ellipsoid to describe the boundary of the anomaly. This model has the effect of regularizing the inversion problem and provides a natural means of including additional physical properties if they are known a priori. A Gauss-Newton-type algorithm with line search is implemented to solve the underlying nonlinear least-squares problem and thereby determine the coefficients of the parameterizations and the descriptors of the ellipsoid. Numerical results show the effectiveness of this method.
我们提出了一种基于形状的方法，用于从漫射光学数据进行三维图像重建。我们的方法与文献中的其他方法不同之处在于，我们同时联合重建物体和背景的特征及定位，而不是依次处理光学属性并对边缘进行后处理。我们算法的效率和稳健性的关键在于我们为背景和异常的光学属性所提出的模型：我们对背景使用低阶参数化，对异常内部使用另一种参数化，并且我们使用一个椭球体来描述异常的边界。该模型具有使反演问题正则化的效果，并且如果先验知道额外的物理属性，还提供了纳入这些属性的自然方式。实现了一种带有线搜索的高斯 - 牛顿型算法来解决潜在的非线性最小二乘问题，从而确定参数化的系数和椭球体的描述符。数值结果表明了该方法的有效性。
