Foygel Barber Rina, Sidky Emil Y, Gilat Schmidt Taly, Pan Xiaochuan
Department of Statistics, The University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA.
Phys Med Biol. 2016 May 21;61(10):3784-818. doi: 10.1088/0031-9155/61/10/3784. Epub 2016 Apr 15.
We develop a primal-dual algorithm that allows for one-step inversion of spectral CT transmission photon counts data to a basis map decomposition. The algorithm allows for image constraints to be enforced on the basis maps during the inversion. The derivation of the algorithm makes use of a local upper bounding quadratic approximation to generate descent steps for non-convex spectral CT data discrepancy terms, combined with a new convex-concave optimization algorithm. Convergence of the algorithm is demonstrated on simulated spectral CT data. Simulations with noise and anthropomorphic phantoms show examples of how to employ the constrained one-step algorithm for spectral CT data.
我们开发了一种原始对偶算法，该算法允许将光谱CT透射光子计数数据一步反演为基图分解。该算法在反演过程中允许对基图施加图像约束。算法的推导利用局部上界二次近似来为非凸光谱CT数据差异项生成下降步长，并结合一种新的凸凹优化算法。在模拟光谱CT数据上证明了该算法的收敛性。带有噪声和人体模型的模拟展示了如何将约束一步算法应用于光谱CT数据的示例。
