Efficient noise filtering is the difficulty of image denoising on the premise of preserving the edge and internal texture information of the image. Therefore, this paper focused on adaptive Gaussian variational model and block matching image denoising method in the wave domain from the non-local point of view. At first, a 3D block match harmonic filtering model was establish in that wavelet domain, 3D transform was use to represent that real signals in the match block group in a sparse form, then the shrinkage threshold was used to achieve the purpose of pre-denoising, and the wavelet transform was then used to extract the high frequency part of the predictor image for filtering. In order to avoid edge blurring, Laplace-Gaussian algorithm was used to construct a new operator into the diffusion model, and the wavelet coefficients were reconstructed to obtain the final approximation of the original image. Secondly, a block matching denoising model based on shear wave was proposed. In order to avoid ill-conditioned problem, The multi-scale geometric analysis method using shearlet transform can improve the edge protection ability, and a block matching denoising model based on shearlet is proposed. The new model predicts the scaling threshold according to the statistical characteristics of the histogram, performs hard threshold filtering on the high-frequency sub-band to obtain the processed subband coefficients, and performs block matching 3D filtering on the decomposed low-frequency sub-band coefficients to obtain the processed coefficients. All processed subband coefficients are inversely transformed and reconstructed to obtain a denoised image. The analysis and simulation results showed that the two new models can effectively suppress noise and improve the clarity, and the block matching denoising based on shear wave had more advantages.