Spectral X-ray Imaging and Phase Retrieval

X-ray phase-contrast imaging (XPCI) is a promising modality sensitive to fine structures that are often invisible with traditional absorption-only X-ray imaging. However, since XPCI depends on two contrast mechanisms (absorption and phase), it in principle requires multiple independent measurements for accurate reconstruction. With emerging photon-counting detectors available to conveniently provide multiple energy measurements in a single shot, spectral XPCI has emerged as a promising candidate for quantitative phase retrieval.

Taken separately, spectral imaging and XPCI each aim to improve soft-tissue image quality, but they face distinct challenges: limited native soft-tissue sensitivity and the need for multiple measurements, respectively. The combined spectral XPCI approach could offer new advantages while resolving these same limitations. While previous spectral XPCI material decomposition approaches have demonstrated the technique's potential to improve image quality, they typically rely on inverting relatively idealized and simplified forward models. This is likely due to the lack of an analytical solution for a full polychromatic system model and the computational challenges of developing a numerical or machine-learning based solution in the context of XPCI.

The purpose of this dissertation is to unite traditional spectral X-ray imaging with the emerging field of XPCI through the lens of material decomposition. In part one, we focus on absorption-contrast imaging, using the Cramér–Rao lower bound (CRLB) to assess and optimize dual-energy CT systems with megavoltage and kilovoltage spectra for improved radiotherapy imaging. Part two expands the scope to include propagation-based phase contrast, developing a spectral XPCI CRLB model and other simulation-based metrics for assessing basis material image quality. We utilize these to examine the common assumptions underlying existing spectral phase-retrieval and material-decomposition methods. Finally, in part three, we propose an improved material decomposition framework for spectral XPCI based on a more generalizable optimization-based approach. Using an iterative solution enables the inversion of a more wholistic forward model, bypassing common simplifying approximations required by existing closed-form inversions over parameter ranges typical of both current and novel sub-micron X-ray imaging systems. This work lays the foundation for future work aiming to more fully realize the benefits of spectral imaging through quantitative phase retrieval and material decomposition.