Multi-Channel Potts-Based Reconstruction for Multi-Spectral Computed Tomography
This work addresses image reconstruction challenges in multi-spectral CT for medical or material imaging, but it is incremental as it builds on existing Potts and TV priors with specific adaptations.
The paper tackled the problem of reconstructing multi-channel images in multi-spectral CT by exploiting structural correlations between channels, using a multi-channel Potts prior to enforce piecewise constant solutions with aligned edges, and achieved improved reconstruction for compound solid bodies compared to TV-based methods in numerical experiments.
We consider reconstructing multi-channel images from measurements performed by photon-counting and energy-discriminating detectors in the setting of multi-spectral X-ray computed tomography (CT). Our aim is to exploit the strong structural correlation that is known to exist between the channels of multi-spectral CT images. To that end, we adopt the multi-channel Potts prior to jointly reconstruct all channels. This prior produces piecewise constant solutions with strongly correlated channels. In particular, edges are enforced to have the same spatial position across channels which is a benefit over TV-based methods. We consider the Potts prior in two frameworks: (a) in the context of a variational Potts model, and (b) in a Potts-superiorization approach that perturbs the iterates of a basic iterative least squares solver. We identify an alternating direction method of multipliers (ADMM) approach as well as a Potts-superiorized conjugate gradient method as particularly suitable. In numerical experiments, we compare the Potts prior based approaches to existing TV-type approaches on realistically simulated multi-spectral CT data and obtain improved reconstruction for compound solid bodies.