Model-Based Approaches to Ill-Conditioned Inverse Problems in X-Ray Imaging

X-ray Computed Tomography (XCT) is a widely used non-destructive imaging technique. With advancements in hardware technology, including X-ray source and detector improvements, there is increasing demand for higher spatial resolution, faster acquisition times, and enhanced imaging quality. Moreover, customers seek better performance by addressing challenges such as metal artifacts and imaging low-attenuation objects. These evolving requirements have intensified the need to solve many ill-conditioned inversion problems inherent in X-ray imaging, driving innovations in algorithm development.

This thesis introduces model-based approaches to address two ill-conditioned inverse problems in X-ray imaging. In the first portion of the thesis, we address the inverse problem of estimating the effective spectrum for different X-ray systems using transmission CT measurement of homogeneous metal rods with known material and dimensions. We proposed two approaches to estimate the effective spectrum. First, we propose a dictionary-based spectral estimation (DictSE) algorithm that represents the unknown spectral response using an over-complete dictionary and finds the optimal sparse representation of the spectrum. Second, we propose a model-based spectral calibration (MBSC) algorithm that models the effective spectrum as a function of some physically meaningful parameters and estimates the spectral response by estimating a limited number of parameters with multi-voltage or multi-filtration dataset. Using simulated and measured data, we demonstrate that MBSC outperforms other methods' accuracy and robustness.

In the second portion of the thesis, we address the inverse problem of reconstructing images from sparse-view CT scans, a critical task in many applications to achieve faster acquisition times. We propose a direct reconstruction method called Recurrent Stacked Back Projection (RSBP), which leverages a deep recurrent neural network on the Stacked Back Projections (SBP) to improve reconstruction quality. Using simulated and experimental data, we demonstrate that our method produces more high-quality reconstructions from sparse measurements than the reconstructions from filter backprojection (FBP) and model-based iterative reconstruction (MBIR).