An Overview of CT Reconstruction with Applications to Photon Counting Detectors

X-ray computed tomography (CT) has now become a mainstay of radiology and medical diagnosis. While the theory of CT reconstruction has been described in detail in the form of textbooks and various review articles, the basic concepts of reconstruction are sometimes mysterious to developers of PCD technology. The goal of this chapter is to demystify some elements of CT reconstruction by providing a brief tutorial and overview, so that detector subsystem experts such as ASIC designers and high-Z semiconductor specialists can better understand the systems trade-offs that they face. We seek to provide a working understanding only, not a complete mathematical derivation. The discussion will be centered on new applications provided by PCD technology. In this chapter, we will provide a working overview of CT reconstruction, starting from the foundational projection-slice theorem and ending with a qualitative understanding of helical reconstruction, iterative reconstruction, and deep learning denoising. We will especially elaborate on the higher spatial resolution of PCD CT and how this affects reconstruction. We will further describe spectral reconstruction and how multibin data are transformed into spectral images. Finally, we will close with some practical comments on how PCD data would be used in practice and how knowledge of CT reconstruction could affect PCD subsystem design.