基于梯度下降法的双能CT双物质分解算法

Two-Material Decomposition Algorithm of Dual-Energy CT Based on Gradient Descent Method

基物质分解是双能CT重建的重要步骤,其中双物质分解是常用的分解模型之一,该模型的核心关键是计算分解系数投影.为了更快计算它,提出了基于误差反馈梯度下降的双能CT双物质分解算法和基于Armijo-Goldstein梯度下降的双能CT双物质分解算法.由于计算了梯度下降步长,这两种方法能快速迭代求解基物质分解系数投影.同时他们有效地解决了双能CT重建的非线性问题.仿真实验结果显示,与传统查表匹配法相比,这两种算法稳定收敛,计算速度快,重建精度高,对临床应用有重要的意义.在重建结果精度近似的情况下,基于Armijo-Goldstein梯度下降的算法采用不精确线性搜索步长,因此它的运行速度更快.

Basis material decomposition is a very essential step in dual-energy CT （ D E C T ） reconstruction and two-material decomposition is one of the most common model whose key point is to obtain the projections of decomposition coefficient. To improve the speed of it, two-material decomposition algorithms were proposed,which are the dual-energy CT based on the error feedback gradient descent method and the Armijo-Goldstein rule gradient descent method, respectively. These two methods were able to get the projections of decomposition coefficient quickly because of the computed step size in gradient descent. Moreover, the nonlinear problem in dual-energy CT reconstruction was also effectively and efficiently solved by using the proposed methods. Simulation results indicated that compared to the projection matching method,the two proposed methods can get stable convergence and high reconstruction precision with a short span of time, which has an important significance to the clinical application. With the same reconstruction precision, the algorithm based on the Armijo-Goldstein rule gradient descent is faster, using the inexact linear search step size.