质子CT图像重建的迭代最小二乘法
An Iterative Least Squares Method for Proton CT Image Reconstruction
摘要：
临床上有用的质子计算机断层成像图像将依赖于算法来找到最佳地拟合测量的质子数据的三维质子阻止本领分布。我们提出了一个最小二乘迭代方法与许多功能，把质子成像到一个更定量的框架。这些包括最佳地拟合质子的唯一解的定义、考虑质子测量不确定性的迭代向量的定义、单独地针对每个迭代的最佳步长的定义、同时优化许多迭代的步长的能力、将质子数据划分成用于并行处理的任意数量的块的能力以及图形处理单元的使用，以及停止标准的定义，以确定何时停止迭代。我们发现，它是可能的，对于任何对象被成像，以提供保证，图像是量化接近最佳解决方案，和步长的优化减少了收敛所需的迭代总数。我们证明了使用这些算法的真实数据。
英文摘要：
Clinically useful proton Computed Tomography images will rely on algorithms to find the three-dimensional proton stopping power distribution that optimally fits the measured proton data. We present a least squares iterative method with many features to put proton imaging into a more quantitative framework. These include the definition of a unique solution that optimally fits the protons, the definition of an iteration vector that takes into account proton measurement uncertainties, the definition of an optimal step size for each iteration individually, the ability to simultaneously optimize the step sizes of many iterations, the ability to divide the proton data into arbitrary numbers of blocks for parallel processing and use of graphical processing units, and the definition of stopping criteria to determine when to stop iterating. We find that it is possible, for any object being imaged, to provide assurance that the image is quantifiably close to an optimal solution, and the optimization of step sizes reduces the total number of iterations required for convergence. We demonstrate the use of these algorithms on real data.
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