Joint Statistical Iterative Material Image Reconstruction for Spectral Computed Tomography Using a Semi-Empirical Forward Model

By acquiring tomographic measurements with several distinct photon energy spectra, spectral computed tomography (spectral CT) is able to provide additional material-specific information compared with conventional CT. This information enables the generation of material selective images, which have found various applications in medical imaging. However, material decomposition typically leads to noise amplification and a degradation of the signal-to-noise ratio. This is still a fundamental problem of spectral CT, especially for low-dose medical applications. Inspired by the success for low-dose conventional CT, several statistical iterative reconstruction algorithms for spectral CT have been developed. These algorithms typically rely on detailed knowledge about the spectrum and the detector response. Obtaining this knowledge is often difficult in practice, especially if photon counting detectors are used to acquire the energy specific information. In this paper, a new algorithm for joint statistical iterative material image reconstruction is presented. It relies on a semi-empirical forward model which is tuned by calibration measurements. This strategy allows to model spatially varying properties of the imaging system without requiring detailed prior knowledge of the system parameters. We employ an efficient optimization algorithm based on separable surrogate functions to accelerate convergence and reduce the reconstruction time. Numerical as well as real experiments show that our new algorithm leads to reduced statistical bias and improved image quality compared with projection-based material decomposition followed by analytical or iterative image reconstruction.