Spatially varying regularization weights for one-step spectral CT with SQS

Photon-counting detectors provide spectral information for x-ray acquisitions. Taking advantage of this information currently requires iterative algorithms to reconstruct basis material CT images. One-step reconstruction is the simultaneous inversion of the spectral distortion occurring in the detector and the geometrical projection. Separable quadratic surrogate (SQS) algorithms have been applied to this one-step problem with satisfactory convergence and material separation. However, this class of method leads to numerical instabilities stemming from voxels out of the field-of-view (FOV) which need to be included in the forward model for reconstructing the FOV. We aim at improving one-step spectral CT reconstruction by investigating two possible corrections of this effect: replacing the exponential in the forward model by a linear function for negative attenuations and spatially varying regularization depending on the geometrical conditioning. We demonstrate the efficiency of the second method using experimental data acquired on a clinical prototype CT scanner with a photon-counting detector.