AFIRE: Accurate and Fast Image Reconstruction Algorithm for Geometric-inconsistent Multispectral CT

Abstract

For nonlinear multispectral computed tomography (CT), accurate and fast image reconstruction is challenging when the scanning geometries under different X-ray energy spectra are inconsistent or mismatched. Motivated by this, we propose an Accurate and Fast Image REconstruction (AFIRE) algorithm to address such problems in the case of mildly full scan. From the continuous (resp. discrete) setting, we discover that the derivative operator (gradient) of the involved nonlinear mapping at some special points, for example, at zero, can be represented as a composition (block multiplication) of a diagonal operator (matrix) composed of X-ray transforms (projection matrices) and a very small-scale matrix. Based on these insights, the AFIRE algorithm is proposed by leveraging the simplified Newton method. Under proper conditions, we establish the convergence theory of the proposed algorithm. Furthermore, numerical experiments are also carried out to verify that the proposed algorithm can accurately and effectively reconstruct the basis images in completely geometric-inconsistent dual-energy CT with noiseless and noisy projection data. Particularly, the proposed algorithm significantly outperforms some state-of-the-art methods in terms of accuracy and efficiency. Finally, the flexibility and extensibility of the proposed algorithm are also demonstrated.