Abstract: Total variation (TV) minimum algorithm is an image reconstruction algorithm based on compressed sensing theory, which can realize the reconstruction of images with high accuracy from sparse projection or noisy projection data and has been widely used in computed tomography (CT), magnetic resonance imaging (MRI) and electronic paramagnetic resonance imaging (EPRI). Energy spectrum CT, T1 or T2 weighted MRI and EPRI both belong to multi-channel imaging. The channel-by-channel TV algorithm can achieve high-precision image reconstruction, but it ignores the similarity among the images of each channel while Nuclear TV algorithm is a TV algorithm that considers the image similarity among channels, and can realize high-precision image reconstruction. For multi-channel image reconstruction, taking CT reconstruction as an example, this paper proposes a nuclear TV multi-channel image reconstruction algorithm based on the framework of Chambolle-pock algorithm. Through the reconstruction experiments of simulated phantom and real CT image phantom, the accuracy of the algorithm is verified, the convergence of the algorithm is analyzed, the influence of algorithm parameters on the convergence rate is explored, and the sparse reconstruction ability and noisy projection reconstruction ability of the algorithm are evaluated. The experimental results show that the proposed algorithm can achieve higher reconstruction accuracy than the channel-by-channel TV algorithm. Nuclear TV algorithm is a high-precision multi-channel image reconstruction algorithm, which can be applied to multi-channel reconstruction of various imaging modes.