The problem of Poisson tensor completion aims to recover a tensor from partial observations in the presence of Poisson noise. Existing approaches utilized the transformed tensor nuclear norm to explore the low-rankness of a tensor, which is the \(\ell _1\) norm of singular values vectors of all frontal slices of a tensor in the transformed domain. Nevertheless, the \(\ell _1\) norm is suboptimal due to its biased estimate. In this paper, we propose a nonconvex model based on transformed tensor nuclear norm for Poisson tensor completion. In order to explore the global low-rankness of the underlying tensor, a family of nonconvex functions are employed onto the singular values of all frontal slices of a tensor in the transformed domain. Furthermore, the nonlocal self-similarity is incorporated into the nonconvex model to describe the similar structures and characterize the intrinsic details of multi-dimensional images. A proximal alternating minimization algorithm is developed to solve the resulting models, whose convergence is established under very mild conditions. Extensive numerical examples on hyperspectral images, video images, and fluorescence microscope images demonstrate that the proposed approach outperforms several state-of-the-art methods.
