Iterative Reconstruction in Multispectral Computerized Tomography

Computerized Tomography(CT) is widely applied in medical imaging and industrial cases for non-invasive/non-destructive studies of varying materials. Bayesian statistical, algebraic approaches to image reconstruction have shown potential to better control noise and improve resolution relative to conventional, single pass methods. The first stage of this work verifies the viability of Bayesian estimation in several cases with single-energy data using synthetic data and scans from medical CT and security-focused systems. Due to advancements in detector technology, energy-specific information can be extracted from scans, yielding separate datasets for each of many energy levels of X-ray energy. This higher-dimensional data provides potentially distinct reconstructions for different materials. This thesis presents a generalization of existing algebraic reconstruction to directly calculate the material decomposition of an object, with the sinogram partitioned into predefined energy bins as input. Iterative Coordinate Descent (ICD) is expanded to a Newton-Raphson like optimization in the space of the fractional content of known materials. Preliminary results under quadratic regularization demonstrate rapid, reliable convergence to images of three materials from five energy bins. Comparisons are provided with existing reconstruction methods.