Statistical Reconstruction Algorithms for Polyenergetic X-ray Computed Tomography

X-ray Computed Tomography Statistical Iterative Reconstruction byIdris A. Elbakr Chair: Jeffrey A. Fessler Statistical reconstruction for transmission tomography is emerging as potential al-ternative to conventional analytic image reconstruction. To fully realize their poten-tial in noise reduction and image quality improvement, statistical algorithms shouldbe based upon a system model that incorporates measurement statistics, attenuationphysics 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 Poissonstatistics. We derive the compound Poisson probability mass function and a practicalbut approximate likelihood. The likelihood is based on a statistical model thataccounts for energy-dependent statistics, Poisson scintillation light and electronicadditive Gaussian noise. We compare the approximate likelihood with the ordinaryPoisson and exact likelihoods. The approximate likelihood is more accurate than the ordinary Poisson likelihood in low count situations, and may be useful for imagereconstruction in such situations.We derive a polyenergetic statistical X-ray CT reconstruction algorithm. Thealgorithm is based on polyenergetic X-ray attenuation physics and has been derivedfor objects containing an arbitrary number of materials. The algorithm derivationinvolves successive application of the optimization transfer principle to arrive ata simple and easy to maximize cost function. The algorithm requires knowledgeof the X-ray spectrum or related measurements and a pre-segmented map of thedistributions of different tissues within the image. Such a map is available from FBPreconstruction. The pre-segmentation map keeps the number of unknowns in thereconstruction problem equal to the number of pixels. In this regard the algorithmis comparable to conventional beam hardening correction methods. The algorithmis a gradient descent algorithm that can be accelerated using ordered subsets anda precomputed curvature. It is also possible to derive a curvature that guaranteesmonotonicity. We use the algorithm to reconstruct objects that contain materialsthat can be categorized as bone and (water-like) soft tissue. The iterative algorithmis superior to conventional beam hardening reduction methods in terms of artifactsuppression and noise reduction.To relax the requirement for a pre-segmentation map, we propose object modelsthat parameterize the scanned object in terms of spatial and energy components. Theobject models keep the number of unknowns equal to the number of pixels, whichis necessary if one does not wish to rely on multiple-energy scans. The models arebased on the attenuation properties of tissues, and allow pixels to contain mixturesof tissues. This is accomplished by restricting the tissue fractions at each pixel to be(known) functions of the pixel density. We develop models (for two base materials) suitable for distinct anatomical structures as well as for objects better characterizedas mineral solutions in water. The segmentation-free iterative algorithms performbetter than the FBP pre-segmented iterative algorithm and conventional beam hard-ening correction methods. Moreover, the segmentation-free algorithm is not hypersensitive to mismatch between the model spectrum and the actual tube spectrum.We also develop a system model for the GE LightSpeed CT scanner (GeneralElectric Medical Systems, Milwaukee, WI) by examining spurious effects for whichCT measurements are typically corrected. The system model accounts for first or-der polyenergetic effects, X-ray tube off-focal radiation and detector afterglow. Apenalized likelihood algorithm based on the system model gives promising noise per-formance results, when compared to FBP. Image reconstruction of a large asymmetricobject produces a shading artifact, that may be due to a mismatch in the measure-ments forward model. Eliminating the shading artifact and improving the forwardmodel are important future work topics.The performance of the proposed algorithms are examined with simulation andreal data. The polyenergetic statistical algorithm is effective in suppressing beamhardening artifacts. Its performance is shown to be comparable to a statistical al-gorithm based on an idealized oracle segmentation. The algorithm with an objectmodel for mineral solutions is promising for quantitative applications, and is shownto estimate mineral solution density values within 1%.