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3 July 2001 Statistical x-ray-computed tomography image reconstruction with beam- hardening correction
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Abstract
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 non-overlapping 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.
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Idris A. Elbakri and Jeffrey A. Fessler "Statistical x-ray-computed tomography image reconstruction with beam- hardening correction", Proc. SPIE 4322, Medical Imaging 2001: Image Processing, (3 July 2001); https://doi.org/10.1117/12.430961
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