Regularized Statistical Material Decomposition in Medical Imaging

In viewing underlying pathology with medical imaging, often specific material components contain most of the diagnostic information. Therefore, material component separation is desirable in many medical applications. Recent generations of MRI and X-ray CT systems can collect multiple measured data sets by changing data acquisition parameters, e.g., pulse sequence timing parameters in MRI and X-ray tube voltage in CT. These systems allow one to separate images of material components.;In this thesis, we present novel image decomposition methods for MRI and X-ray CT applications. These methods use regularization and multiple data sets. We also propose iterative algorithms to minimize appropriate regularized least-squares cost functions. In MR imaging, we investigated penalized-likelihood approaches that can jointly estimate water components, fat components, and field map. The methods lead to improved chemical components estimates by using regularization of the filed map. In dual-energy CT reconstruction, we proposed a penalized weighted least square method that separates two material density maps from fast kVp-switched sinograms without any interpolation. We also developed a novel iterative algorithm that estimates material sinograms from raw DE CT data directly without using a logarithm that is sensitive to noise. Experiments on synthetic data and phantom data suggest that our methods improve the quality and accuracy of the estimated images compared to conventional methods for material separation.