  Compressive sensing (CS) based computed tomography (CT) image reconstruction
aims at reducing the radiation risk through sparse-view projection data. It is
usually challenging to achieve satisfying image quality from incomplete
projections. Recently, the nonconvex ${{L_ {{1/2}}}} $-norm has achieved
promising performance in sparse recovery, while the applications on imaging are
unsatisfactory due to its nonconvexity. In this paper, we develop a ${{L_
{{1/2}}}} $-regularized nonlocal self-similarity (NSS) denoiser for CT
reconstruction problem, which integrates low-rank approximation with group
sparse coding (GSC) framework. Concretely, we first split the CT reconstruction
problem into two subproblems, and then improve the CT image quality furtherly
using our ${{L_ {{1/2}}}} $-regularized NSS 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 ${{L_ {{1/2}}}} $
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.
