  Low-dose CT image reconstruction has been a popular research topic in recent
years. A typical reconstruction method based on post-log measurements is called
penalized weighted-least squares (PWLS). Due to the underlying limitations of
the post-log statistical model, the PWLS reconstruction quality is often
degraded in low-dose scans. This paper investigates a shifted-Poisson (SP)
model based likelihood function that uses the pre-log raw measurements that
better represents the measurement statistics, together with a data-driven
regularizer exploiting a Union of Learned TRAnsforms (SPULTRA). Both the SP
induced data-fidelity term and the regularizer in the proposed framework are
nonconvex. The proposed SPULTRA algorithm uses quadratic surrogate functions
for the SP induced data-fidelity term. Each iteration involves a quadratic
subproblem for updating the image, and a sparse coding and clustering
subproblem that has a closed-form solution. The SPULTRA algorithm has a similar
computational cost per iteration as its recent counterpart PWLS-ULTRA that uses
post-log measurements, and it provides better image reconstruction quality than
PWLS-ULTRA, especially in low-dose scans.
