Moreau-envelope-enhanced Nonlocal Shearlet Transform and Total Variation for Sparse-View CT Reconstruction

Iterative computed tomography (CT) image reconstruction with sparse regularization can substantially reduce the amount of projection data. However, when the sparse-view sampled projection data are noisy, it is challenging to achieve satisfactory reconstruction with local prior-based sparsity regularization such as total variation. This is because employing local prior information, it is difficult to distinguish structural details from noise. In this work, to address the problem, a nonlocal 3D shearlet sparse regularization based on image patch matching and a patch-based shearlet transform is proposed for sparse-view CT image reconstruction, which can effectively utilize nonlocal self-similar prior information to restore the structural details of CT images with sparse-view noisy projection data. As the shearlet transform belongs to a multi-scale directional sensitive transform, it can better preserve the anisotropic features of the image compared with a traditional wavelet transform. Moreover, we incorporate the proposed nonlocal shearlet regularization as an L-1 regularization term into the TV-L-1 model to further help preserve the edge of the reconstructed image. In addition, the Moreau-envelope-enhanced L-1 norm is also employed to enhance the performance of the reconstruction. The simulation and practical data study show that the proposed method can effectively suppress noise and protect the fine structures, leading to an overall improvement in the quality of the reconstructed image.