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Compressive sensing (CS) based computed tomography (CT) image reconstructionaims at reducing the radiation risk through sparse-view projection data. It isusually challenging to achieve satisfying image quality from incompleteprojections. Recently, the nonconvex ${{L_ {{1/2}}}} $-norm has achievedpromising performance in sparse recovery, while the applications on imaging areunsatisfactory due to its nonconvexity. In this paper, we develop a ${{L_{{1/2}}}} $-regularized nonlocal self-similarity (NSS) denoiser for CTreconstruction problem, which integrates low-rank approximation with groupsparse coding (GSC) framework. Concretely, we first split the CT reconstructionproblem into two subproblems, and then improve the CT image quality furtherlyusing our ${{L_ {{1/2}}}} $-regularized NSS denoiser. Instead of optimizing thenonconvex problem under the perspective of GSC, we particularly reconstruct CTimage via low-rank minimization based on two simple yet essential schemes,which build the equivalent relationship between GSC based denoiser and low-rankminimization. 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 withthe CT reconstruction problem by alternating direction method of multipliers(ADMM) framework. Extensive experimental results on typical clinical CT imageshave demonstrated that our approach can further achieve better performance thanpopular approaches.

Nonconvex ${{L_ {{1/2}}}} $-Regularized Nonlocal Self-similarity Denoiser for Compressive Sensing based CT Reconstruction