A deep learning one-step solution to material image reconstruction in photon counting spectral CT

Photon counting detectors in x-ray computed tomography (CT) are a major technological advancement that provides additional energy information and improves the decomposition of the CT image into material images. One important challenge in this new modality is how best to perform tomographic reconstruction. As a result of measuring multiple projections from different energy bins, more complex reconstruction algorithms are required. These are computationally demanding, due to the their large number of degrees of freedom. Also, the reconstruction algorithm needs to output multi-material image solutions. Reconstruction algorithms for spectral CT divide into two paradigms: two-step and one-step. Most typical solution is the two-step approach, where a first step consists of a material decomposition in projection domain, and a second step on tomographic reconstruction of each projection. This solution is computationally tractable but can cause a loss of information and it is difficult to regularize. The one-step solution, on the other hand, solves a joint optimization material decomposition and reconstruction, it is solved iteratively and can be, however, very time consuming. We present a deep learning-based solution to the one-step problem, with an architecture that mimics the updates of a primal-dual solver, and has demonstrated much greater computational efficiency than model-based iterative reconstruction. We have studied a proof-of-concept on a set of 700 Shepp-Logan phantoms. Our approach has shown enhanced performance compared to a model-based two-step approach, as well as compared to considering deep learning only in the first step of the two-step solution.