In view of the structural residual noise in the weighted nuclear norm minimization algorithm and the inability to maintain the edge structure of the image, a denoising method that minimizes the weighted kernel norm and improves the wavelet threshold was adopted. The total variation model to perform preliminary denoising of the noise image, and the noisy image to subtract the preliminary denoised image were used. An improved wavelet threshold function was used to denoise the noise difference image obtained after subtraction. The denoised residual image was superimposed with the preliminary denoised image, and the superimposed image was finally denoised using an iterative weighted kernel norm minimization algorithm based on the residual noise level. Compared with the more popular denoising algorithms, the PSNR and SSIM processed by this algorithm are improved, the texture structure of the image can be maintained, and the effect is better in a high-noise environment.