Efficient and accurate likelihood for iterative image reconstruction in x-ray computed tomography

We report a novel approach for statistical image reconstruction in X-ray CT. Statistical image reconstruction depends on maximizing a likelihood derived from a statistical model for the measurements. Traditionally, the measurements are assumed to be statistically Poisson, but more recent work has argued that CT measurements actually follow a compound Poisson distribution due to the polyenergetic nature of the X-ray source. Unlike the Poisson distribution, compound Poisson statistics have a complicated likelihood that impedes direct use of statistical reconstruction. Using a generalization of the saddle-point integration method, we derive an approximate likelihood for use with iterative algorithms. In its most realistic form, the approximate likelihood we derive accounts for polyenergetic X-rays and Poisson light statistics in the detector scintillator, and can be extended to account for electronic additive noise. The approximate likelihood is closer to the exact likelihood than is the conventional Poisson likelihood, and carries the promise of more accurate reconstruction, especially in low X-ray dose situations.