Statistical X-ray computed tomography image reconstruction with beam hardening correction

This paper describes two statistical iterative reconstruction methods for X-ray CT. The first method assumes a mono-energetic model for X-ray attenuation. We approximate the transmission Poisson likelihood by a quadratic cost function and exploit its convexity to derive a separable quadratic surrogate function that is easily minimized using parallelizable algorithms. Ordered subsets are used to accelerate convergence. We apply this mono-energetic algorithm (with edge-preserving regularization) to simulated thorax X-ray CT scans. A few iterations produce reconstructed images with lower noise than conventional FBP images at equivalent resolutions. The second method generalizes the physical model and accounts for the poly-energetic X-ray source spectrum and the measurement nonlinearities caused by energy-dependent attenuation. We assume the object consists of a given number of nonoverlapping tissue types. The attenuation coefficient of each tissue is the product of its unknown density and a known energy-dependent mass attenuation coefficient. We formulate a penalized-likelihood function for this poly-energetic model and develop an iterative algorithm for estimating the unknown densities in each voxel. Applying this method to simulated X-ray CT measurements of a phantom containing both bone and soft tissue yields images with significantly reduced beam hardening artifacts.