McCann Michael T, Nilchian Masih, Stampanoni Marco, Unser Michael
Opt Express. 2016 Jun 27;24(13):14564-81. doi: 10.1364/OE.24.014564.
We present a fast algorithm for fully 3D regularized X-ray tomography reconstruction for both traditional and differential phase contrast measurements. In many applications, it is critical to reduce the X-ray dose while producing high-quality reconstructions. Regularization is an excellent way to do this, but in the differential phase contrast case it is usually applied in a slice-by-slice manner. We propose using fully 3D regularization to improve the dose/quality trade-off beyond what is possible using slice-by-slice regularization. To make this computationally feasible, we show that the two computational bottlenecks of our iterative optimization process can be expressed as discrete convolutions; the resulting algorithms for computation of the X-ray adjoint and normal operator are fast and simple alternatives to regridding. We validate this algorithm on an analytical phantom as well as conventional CT and differential phase contrast measurements from two real objects. Compared to the slice-by-slice approach, our algorithm provides a more accurate reconstruction of the analytical phantom and better qualitative appearance on one of the two real datasets.
我们提出了一种用于传统和差分相衬测量的全三维正则化X射线断层扫描重建的快速算法。在许多应用中，在产生高质量重建的同时降低X射线剂量至关重要。正则化是实现这一目标的绝佳方法，但在差分相衬情况下，它通常以逐片方式应用。我们建议使用全三维正则化来改善剂量/质量权衡，这是逐片正则化无法实现的。为了使这在计算上可行，我们表明迭代优化过程的两个计算瓶颈可以表示为离散卷积；由此产生的用于计算X射线伴随算子和正规算子的算法是比重新网格化更快、更简单的替代方法。我们在一个解析体模以及来自两个真实物体的传统CT和差分相衬测量上验证了该算法。与逐片方法相比，我们的算法在解析体模上提供了更准确的重建，并且在两个真实数据集中的一个上具有更好的定性外观。
