Alternating Minimization Based Framework for Simultaneous Spectral Calibration and Image Reconstruction in Spectral CT

Photon-counting detectors acquire spectral information for the scanned object by separating incoming photons into pre-defined energy windows based on their energies. Using this energy information in computed tomography (CT) imaging, also called spectral CT, can mitigate beam-hardening artifacts and allows to estimate two or more basis material maps from the measured counts data. An important step for realizing spectral CT with photon-counting detectors is calibrating the spectral response of the imaging system. In this work, we explore the use of KL-divergence approach for spectrum estimation to allow for auto-calibration of the spectral response of each of the detector pixels in the spectral CT image reconstruction. Specifically, we incorporate unknown spectral components in the spectral CT data model and formulate simultaneous image reconstruction and estimation of these spectral components into the framework of alternating minimization. A simulation study is carried out to show how the algorithm can be implemented on spectral CT data.