A new linearized split Bregman iterative algorithm for image reconstruction in sparse-view X-ray computed tomography

In this paper, a new linearized split Bregman iterative algorithm is proposed for sparse-view X-ray computed tomography, which can avoid solving a large-scale and unstructured linear system in each iteration. Remarkably, our method can be generalized to efficiently resolve some other image processing and analysis models, for instance, the robust compressed sensing, the total variation-ℓ1ℓ1, and the ℓ1ℓ1–ℓ1ℓ1. We also give rigorous proofs for the convergence of the proposed method under appropriate conditions for the aforementioned problems. Experimental results demonstrate that our algorithm has better performance in terms of reconstruction quality, effectiveness and robustness, compared with some other methods (e.g. gradient-flow-based semi-implicit finite element method, split Bregman, etc.) for the robust image reconstruction in sparse-view X-ray computed tomography.