Tensor-based restoration of medical images and video images was studied with limited samples. On the basis of the theory of tensor singular value decomposition (t-SVD), a tensor rank-correction model (CRTNN) was proposed to correct the tensor nuclear norm minimization model (TNN). A two-stage rank correction method is given as follows: the first stage is used to generate a pre-estimator by solving the TNN model, and the second stage is to solve the CRTNN model to generate a high-accuracy recovery by the pre-estimator. A tensor proximal point algorithm was proposed to solve the CRTNN model and the TNN model, making it possible to calculate tensor directly in the real field. The convergence of the algorithm was proved in theory. Numerical experiments of medical images and video images verify the efficiency of the proposed model and method. The experiment results show that tensor rank-correction model and method can achieve higher-accuracy recovery.