Multi-energy CT based on compression sensing theory with sparse-view sampling can effectively reduce radiation dose and maintain the quality of the reconstructed image. However,when the projection data are noisy, the reconstructed image can be still seriously degraded. In order to address this problem, we extend the total nuclear variation (TNV) regularization and propose the nonlocal total nuclear generalized variation (NLTNGV) regularization term. NLTNGV is constructed by using the low rank property of both the nonlocal Jacobian matrix and the local second derivative of the image at different energy spectrum, which can be seen as a more robust structure similarity measure. By employing NLTNGV,the proposed reconstruction method can effectively utilize the sparsity of nonlocal gradients and local second order derivatives and structural similarity of multi-energy CT images to effectively recover the image structure features in noisy case. The experimental results show that the proposed method can enhance the noise-resistant performance and preserve the fine details of the reconstructed images in comparison with TNV-based method.
