There are many unavoidable noise interferences in image capturing and transmission. In order to make it better for subsequent processing, the noise in the image should be removed in advance. There are many kinds of image noises, mainly including salt & pepper noise and Gaussian noise. This paper focuses on the research of the Gaussian noise removal. It introduces many wavelet threshold denoising algorithms which include global threshold denoising, Maxmin threshold denoising, and BayesShrink threshold denoising. Besides, we make a comparative analysis for these denoising methods. The experimental result shows that the wavelet images denoising algorithm based on Gaussian mixture model has the best performance than other threshold denoising methods in both subjectivity and objectivity.