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

μ=Cmax(m,n)σ
\mu = C\max \left( {\sqrt {\rm{m}} ,\sqrt {\rm{n}} } \right)\sigma

, the optimal results are achieved when C=8 and K values are 13-15. The PSNR index of this paper's algorithm is always greater than 45 when the noise intensity is 0.025-0.1, the highest is 58.817, and the lowest is 45.837. The DN value of the image denoised by the algorithm floats 0.012-0.085 on the basis of the original curve, which is less than 0.1. The performance of the algorithm decreases as the noise becomes more and more complex, and the noise intensity of 0.1 finally drops to 45.837, but the output image is still clear.