Rose Sean, Andersen Martin S, Sidky Emil Y, Pan Xiaochuan
Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois 60637.
Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby 2800, Denmark.
Med Phys. 2015 May;42(5):2690-8. doi: 10.1118/1.4914148.
The authors develop and investigate iterative image reconstruction algorithms based on data-discrepancy minimization with a total-variation (TV) constraint. The various algorithms are derived with different data-discrepancy measures reflecting the maximum likelihood (ML) principle. Simulations demonstrate the iterative algorithms and the resulting image statistical properties for low-dose CT data acquired with sparse projection view angle sampling. Of particular interest is to quantify improvement of image statistical properties by use of the ML data fidelity term.
An incremental algorithm framework is developed for this purpose. The instances of the incremental algorithms are derived for solving optimization problems including a data fidelity objective function combined with a constraint on the image TV. For the data fidelity term the authors, compare application of the maximum likelihood principle, in the form of weighted least-squares (WLSQ) and Poisson-likelihood (PL), with the use of unweighted least-squares (LSQ).
The incremental algorithms are applied to projection data generated by a simulation modeling the breast computed tomography (bCT) imaging application. The only source of data inconsistency in the bCT projections is due to noise, and a Poisson distribution is assumed for the transmitted x-ray photon intensity. In the simulations involving the incremental algorithms an ensemble of images, reconstructed from 1000 noise realizations of the x-ray transmission data, is used to estimate the image statistical properties. The WLSQ and PL incremental algorithms are seen to reduce image variance as compared to that of LSQ without sacrificing image bias. The difference is also seen at few iterations--short of numerical convergence of the corresponding optimization problems.
The proposed incremental algorithms prove effective and efficient for iterative image reconstruction in low-dose CT applications particularly with sparse-view projection data.
作者开发并研究基于数据差异最小化和全变差（TV）约束的迭代图像重建算法。各种算法是通过反映最大似然（ML）原理的不同数据差异度量推导出来的。模拟展示了针对稀疏投影视角采样获取的低剂量CT数据的迭代算法及其所得图像的统计特性。特别令人感兴趣的是量化使用ML数据保真项对图像统计特性的改善。
为此开发了一种增量算法框架。推导了增量算法的实例，用于解决包括与图像TV约束相结合的数据保真目标函数的优化问题。对于数据保真项，作者将以加权最小二乘法（WLSQ）和泊松似然（PL）形式的最大似然原理的应用与未加权最小二乘法（LSQ）的应用进行比较。
增量算法应用于通过模拟乳腺计算机断层扫描（bCT）成像应用生成的投影数据。bCT投影中数据不一致的唯一来源是噪声，并且假设透射x射线光子强度服从泊松分布。在涉及增量算法的模拟中，从x射线透射数据的1000次噪声实现重建的一组图像用于估计图像统计特性。与LSQ相比，WLSQ和PL增量算法在不牺牲图像偏差的情况下降低了图像方差。在少数几次迭代时（相应优化问题未达到数值收敛）也能看到这种差异。
所提出的增量算法在低剂量CT应用中，特别是对于稀疏视图投影数据的迭代图像重建，证明是有效且高效的。
