Statistical reconstruction algorithms for polyenergetic x-ray computed tomography

Statistical reconstruction for transmission tomography is emerging as potential alternative to conventional analytic image reconstruction. To fully realize their potential in noise reduction and image quality improvement, statistical algorithms should be based upon a system model that incorporates measurement statistics, attenuation physics and system parameters. CT measurements are often assumed to follow Poisson statistics. CT detectors, however, are energy integrators that give rise to more complex compound Poisson statistics. We derive the compound Poisson probability mass function and a practical but approximate likelihood. The likelihood is based on a statistical model that accounts for energy-dependent statistics, Poisson scintillation light and electronic additive Gaussian noise. We compare the approximate likelihood with the ordinary Poisson and exact likelihoods. The approximate likelihood is more accurate than the ordinary Poisson likelihood in low count situations, and may be useful for image reconstruction in such situations. We derive a polyenergetic statistical X-ray CT reconstruction algorithm. The algorithm is based on polyenergetic X-ray attenuation physics and has been derived for objects containing an arbitrary number of materials. The algorithm derivation involves successive application of the optimization transfer principle to arrive at a simple and easy to maximize cost function. The algorithm requires knowledge of the X-ray spectrum or related measurements and a pre-segmented map of the distributions of different tissues within the image. Such a map is available from FBP reconstruction. The pre-segmentation map keeps the number of unknowns in the reconstruction problem equal to the number of pixels. In this regard the algorithm is comparable to conventional beam hardening correction methods. The algorithm is a gradient descent algorithm that can be accelerated using ordered subsets and a precomputed curvature. It is also possible to derive a curvature that guarantees monotonicity. We use the algorithm to reconstruct objects that contain materials that can be categorized as bone and (water-like) soft tissue. The iterative algorithm is superior to conventional beam hardening reduction methods in terms of artifact suppression and noise reduction. To relax the requirement for a pre-segmentation map, we propose object models that parameterize the scanned object in terms of spatial and energy components. (Abstract shortened by UMI.)