Tensor-based formulation and nuclear norm regularization for multi-energy computed tomography

TL;DR

This paper introduces a tensor-based iterative reconstruction algorithm for multi-energy CT that employs nuclear norm regularization to improve image quality, especially in low-energy noisy scenarios.

Contribution

It proposes a novel tensor-based regularizer and optimization framework for multi-energy CT reconstruction, leveraging a multi-linear image model and tensor nuclear norm.

Findings

Tensor nuclear norm regularization effectively enhances spectral CT reconstructions.

Combining tensor nuclear norm with total variation improves low-energy image quality.

Simulation results demonstrate the method's potential for noise reduction and image fidelity.

Abstract

The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a tensor-based iterative algorithm that simultaneously reconstructs the X-ray attenuation distribution for each energy. We use a multi-linear image model rather than a more standard "stacked vector" representation in order to develop novel tensor-based regularizers. Specifically, we model the multi-spectral unknown as a 3-way tensor where the first two dimensions are space and the third dimension is energy. This approach allows for the design of tensor nuclear norm regularizers, which like its two dimensional counterpart, is a convex function of the multi-spectral unknown. The solution to the resulting convex optimization problem is obtained using an alternating direction method of multipliers (ADMM) approach. Simulation results shows that the generalized tensor nuclear norm can be used as a stand alone regularization technique for the energy selective (spectral) computed tomography (CT) problem and when combined with total variation regularization it enhances the regularization capabilities especially at low energy images where the effects of noise are most prominent.