Micro-slice images collected under a microscope usually have both Gaussian noise and pepper and salt noise. Shannon-Cosine wavelet with interpolation, smoothness, compact support and normalization characteristics was used to construct multi-scale interpolation wavelet operators, and then a wavelet precise integration method for removing mixed noise in images was constructed. And the pepper and salt noise in the micro-slice image was directly eliminated by setting the sparse representation threshold;Shannon-Cosine wavelet sparse expressions of images were brought directly into the image noise reduction P-M model, and then this model was transformed into a system of nonlinear ordinary differential equations and solved it directly by using the precise integration method, which can achieve edge preservation and noise reduction, and eliminate Gaussian noise in the image. The experimental results showed that the proposed method can preserve various texture structures in locust slice images under the condition of satisfying the requirements of noise reduction. As the variance of Gaussian noise was increased from 0.02 to 0.10, the PSNR value of the denoised image was decreased by 11.67%, which was much lower than that of the other methods. This showed that the method proposed had strong robustness when processing locust slice images. When the image Shannon-Cosine wavelet sparse representation method proposed was used to describe the locust slice image, the number of characteristic pixels only accounted for about 10% of the total number of image pixels, which effectively reduced the scale of the problem and improved the solution efficiency.