Abstract: Sparse view sampling and reducing current of X-ray source can effectively reduce radiation dose of multispectral CT,but it will make the projection data insufficient and noisy,leading to serious degeneration of the reconstructed images.To address this problem,we extend the traditional total nuclear variation(TNV) and propose the nonlocal total nuclear variation(NLTNV) regularization method by employing the low rank property of Jacobian matrix composed of nonlocal gradient vector.The proposed method uses only one regularization term to model three kinds of prior information(the structural similarity along energy dimension,the sparsity of image gradient and the spatial nonlocal self-similarity) to restore image details in low dose case,which can effectively alleviate the problem of using too many regularization parameters in reconstruction model,caused by employing multiple independent regularization terms to model different prior information of multispectral CT image.In addition,the reconstruction model based on NLTNV is a convex model,which guarantees the stability and convergence of the algorithm.The experimental results show that compared with the TNV regularization method,the proposed method can significantly improve the overall quality of the reconstructed images.