The development of computed tomography (CT) image reconstruction methods that
significantly reduce patient radiation exposure while maintaining high image
quality is an important area of research in low-dose CT (LDCT) imaging. We
propose a new penalized weighted least squares (PWLS) reconstruction method
that exploits regularization based on an efficient Union of Learned TRAnsforms
(PWLS-ULTRA). The union of square transforms is pre-learned from numerous image
patches extracted from a dataset of CT images or volumes. The proposed
PWLS-based cost function is optimized by alternating between a CT image
reconstruction step, and a sparse coding and clustering step. The CT image
reconstruction step is accelerated by a relaxed linearized augmented Lagrangian
method with ordered-subsets that reduces the number of forward and back
projections. Simulations with 2-D and 3-D axial CT scans of the extended
cardiac-torso phantom and 3D helical chest and abdomen scans show that for both
normal-dose and low-dose levels, the proposed method significantly improves the
quality of reconstructed images compared to PWLS reconstruction with a
nonadaptive edge-preserving regularizer (PWLS-EP). PWLS with regularization
based on a union of learned transforms leads to better image reconstructions
than using a single learned square transform. We also incorporate patch-based
weights in PWLS-ULTRA that enhance image quality and help improve image
resolution uniformity. The proposed approach achieves comparable or better
image quality compared to learned overcomplete synthesis dictionaries, but
importantly, is much faster (computationally more efficient).

本文提出了一种基于 Union of Learned TRAnsforms 的惩罚加权最小二乘（PWLS）重建方法，可以提高低剂量计算机断层扫描图像的质量，同时减少患者的辐射剂量。