F3-A2/F3-A3: Tensor-based Formulation for Spectral Computed Tomography (CT) with Novel Regularization Techniques

Spectral computed tomography (CT) has become increasingly of interest with the development of photon counting X-ray detector technology. The energy selective measurement capabilities of these devices open the doors to many exciting directions in CT research across a number of fields including security applications. Over the past year our work under ALERT support has been directed at the continued development of tensor-based, iterative algorithms that simultaneously reconstruct the X-ray attenuation distribution in space across a range of energies. This approach has allowed for the design of a number of regularization methods built on low rank assumptions on the multi-spectral unknown. The first approach we developed was based on the use of a nuclear norm penalty in each of the three so-called unfoldings of the tensor. The second method, developed in the past year, makes use of the tensor singular value decomposition (tSVD) developed in [1]. In all cases, reconstruction requires the solution of a convex optimization problem the solution of which is obtained using alternating direction method of multipliers (ADMM) techniques. Simulation results shows that both generalized tensor nuclear norm methods can be used as stand-alone regularization techniques for the energy selective (spectral) computed tomography problem and when combined with total variation regularization both enhance the reconstruction accuracy especially at low energy images where the effects of noise are most prominent. In all cases, our methods clearly outperform the current state of the art techniques based on energy-byenergy filtered backprojection reconstruction.