Statistical Reconstruction and Simultaneous Parameter Estimation for Iterative X-ray Computed Tomography

Statistical iterative image reconstruction methods for X-ray computed tomography (CT) have, over the past few years, shown promise in maintaining diagnostic image quality across a wider range of dosage than has been routinely practical with standard deterministic methods. In this dissertation, iterative reconstruction techniques are modified to attack three limited-information problems: (i) photon starvation due to low signals; (ii) artifacts induced by high attenuation objects and (iii) spatially non-uniform sampling geometry.

Dose reduction in clinical X-ray CT causes low signal-to-noise ratio (SNR) in photon-sparse situations. All techniques meet their limits of practicality when significant portions of the sinogram are near photon starvation. The corruption of electronic noise leads to measured photon counts’ taking on negative values, posing a problem for the log() operation in pre-processing of data. We propose two categories of methods for extremely low-count sinogram pretreatment: an adaptive denoising filter and a pointwise Bayesian inference method. The denoising filter is easy to implement and preserves local statistics, but it introduces correlation between channels and may affect image resolution. The Bayesian inference is a pointwise estimate incorporating a prior model for Poisson rates. Both approaches achieve significant improvements in diagnostic image quality at dramatically reduced dosage.

High-attenuation materials pose significant challenges to CT imaging. Formed of high mass density and high atomic number elements, bones and metals, for example, have high resistance to transmission of photons. Scatter and beam hardening effects are more prominent, raising substantially the importance of the nonlinear relation between line-integral projection estimates and path lengths. As a result, streaking artifacts often appear in reconstructed images along high density directions. In this dissertation, two novel iterative approaches are proposed to reduce such artifacts. One method parameterizes scatter and beam hardening as a locally varying additive Poisson noise, and attempts to estimate the offset as part of the iterative reconstruction loop. The other method uses a prior image to guide both reconstruction and sinogram correction. Artifacts are significantly reduced at little cost in resolution loss.

Cone-beam geometry creates non-uniform spatial sampling rates, which becomes a more pronounced issue as scanners are extended to wider cone angles. While in new, wider-coverage detectors, noise non-uniformity can be mitigated by spatially adaptive regularization design, some data dependent systematic errors are difficult to model deterministically. The detector array is adjusted to accommodate detection efficiency issue at large cone angles. Array modules are compromised to be tilted towards the source, which causes systematic inconsistencies between two module boundaries. To combat the challenge of increased sampling non-uniformity, we propose a joint system parameter estimation with image reconstruction algorithm. Clustering and regularization are used to avoid overfitting and “DC” drift.