Nonconvex L₁/₂- regularized nonlocal self-similarity denoiser for compressive sensing based CT reconstruction

Compressive sensing (CS) based computed tomography (CT) image reconstruction aims at reducing the radiation risk through sparse-view projection data. However, it is challenging to achieve satisfying image quality from incomplete projections. Recent works demonstrate the promising potential of nonconvex L1/2-norm in CS problem, while the applications on medical imaging are constrained by its nonconvexity. In this paper, we develop an L1/2-regularized nonlocal self-similarity (NSS) denoiser based CT reconstruction model, which combines with low-rank approximation and group sparse coding (GSC) framework. Concretely, we firstly split the CT reconstruction problem into two subproblems, then improve CT image quality furtherly using our proposed denoiser. Instead of optimizing the nonconvex problem under the perspective of GSC, we particularly reconstruct CT image via low-rank minimization based on two simple yet essential schemes, which build the equivalent relationship between GSC based denoiser and low-rank minimization. Furtherly, the weighted singular value thresholding (WSVT) operator is utilized to optimize the resulting nonconvex L1/2 minimization problem. Following this, our proposed denoiser is integrated with the CT reconstruction problem by alternating direction method of multipliers (ADMM) framework. Extensive experimental results on typical clinical CT images have demonstrated that our approach can further achieve better performance than popular approaches.This work was supported in part by the Educational Commission of Hunan Province of China under grant 21B0466, the National Natural Science Fund for Youth Programs under Grant 61906067, and the China Postdoctoral Science Foundation under Grant 2019M651415 and Grant 2020T130191