  Statistical image reconstruction (SIR) methods have shown potential to
substantially improve the image quality of low-dose X-ray computed tomography
(CT) as compared to the conventional filtered back-projection (FBP) method for
various clinical tasks. According to the maximum a posterior (MAP) estimation,
the SIR methods can be typically formulated by an objective function consisting
of two terms: (1) data-fidelity (or equivalently, data-fitting or
data-mismatch) term modeling the statistics of projection measurements, and (2)
regularization (or equivalently, prior or penalty) term reflecting prior
knowledge or expectation on the characteristics of the image to be
reconstructed. Existing SIR methods for low-dose CT can be divided into two
groups: (1) those that use calibrated transmitted photon counts (before
log-transform) with penalized maximum likelihood (pML) criterion, and (2) those
that use calibrated line-integrals (after log-transform) with penalized
weighted least-squares (PWLS) criterion. Accurate statistical modeling of the
projection measurements is a prerequisite for SIR, while the regularization
term in the objective function also plays a critical role for successful image
reconstruction. This paper reviews several statistical models on CT projection
measurements and various regularization strategies incorporating prior
knowledge or expected properties of the image to be reconstructed, which
together formulate the objective function of the SIR methods for low-dose X-ray
CT.
