In this paper, based on tensor decomposition, SSTV regular constraints are combined with low-rank 3D tensor for image denoising and the effect of the algorithm is enhanced by the augmented Lagrangian method to construct a hyperspectral image denoising algorithm based on tensor decomposition and full variational constraints. After the algorithm design is completed, image restoration is performed based on the use of objective evaluation, standard mean square error, and peak signal-to-noise ratio to test the specific effect of the algorithm. 2 sets of experiments were designed and analyzed the sensitivity of the algorithm parameters. The test results show that for the penalty parameter