Nonhomogeneous and Nonlinear Methods for Tomographic Estimation

医学诊断和材料无损检测中的各种问题都需要重建对象的一部分或横截面，而不是直接查看其内部。断层成像技术允许进行非侵入性/非破坏性研究，将医疗领域的患者创伤和成本降至最低，并通过将外部测量转换为患者或对象内部的图像来减少许多行业的制造和维护费用。在X射线CT扫描等常见实例中，已建立的计算断层图像的方法不适用于涉及数据短缺或由于测量中的固有误差而对其精确值存在很大不确定性的困难情况。对于这些问题，需要明确考虑测量误差的特征以及所研究的组织或材料的共同行为的算法。贝叶斯层析估计等统计方法带来了很大的改进，但基于齐次随机场模型和固定优化策略的传统估计技术似乎正在接近其改进的极限。该项目正在开发三个主要创新来提高层析成像系统的能力，特别关注于三维应用：(1)非均匀图像截面模型，它允许使用简单的多尺度估计过程来精确估计空间变化的图像特征；(2)快速非线性优化算法，用于最小化使用非高斯先验模型进行MAP估计所产生的非二次函数；(3)基于反投影数据的非线性、非迭代估计的层析重建的新方法。本研究适用于各种发射和透射层析成像问题，特别是三维医学发射层析成像的实验研究。

A variety of problems in both medical diagnostics and nondestructive testing of materials requires the reconstruction of a portion or cross section of an object without directly viewing its interior. Tomographic imaging techniques allow noninvasive/nondestructive studies which minimize patient trauma and cost in the medical domain, and reduce manufacturing and maintenance expenses for many industries by transforming external measurements into images of the interior of the patient or object. The established methods for computing tomographic images in common examples such as x-ray CT scanning are inadequate for difficult cases involving a shortage of data or great uncertainty in their precise values due to inherent error in measurements. For these problems, algorithms are needed which explicitly take into account the characteristics of the measurement errors as well as common behavior of the tissue or materials under study. Much improvement has resulted from statistical methods such as Bayesian tomographic estimation, but conventional estimation techniques, based on homogeneous random field models and fixed optimization strategies, seem to be approaching their limits of improvement. This project is developing three principal innovations to improve the capabilities of tomographic systems, with particular focus on three-dimensional applications: (1) nonhomogeneous image cross section models which allow spatially varying image characteristics to be accurately estimated using a simple multiscale estimation procedure; (2) fast nonlinear optimization algorithms for minimizing the nonquadratic functions that result from MAP estimation with nonGaussian prior models; (3) a novel approach to tomographic reconstruction based on nonlinear, non-iterative estimation from back projection data. This research is applicable to the full range of emission and transmission tomographic problems, with particular experimental focus on 3D medical emission tomography.