Image denoising is a well explored topic. Generally, image denoising approaches can be categorized as spatial domain and transform domain methods according to the image representation. Transform domain methods can be divided into two main groups according to their basis functions. Transform domain methods with data adaptive basis functions and transform domain methods with fixed basis functions. Fixed basis functions transform methods, in which, wavelet transform is the most popular, have been widely used for noise reduction applications due to their features and properties, such as frequency / space separation. Also, due to the non-static nature of natural images and the addition of noise to them, statistical methods have received a lot of attention among transform methods. In the present paper, after a brief introduction of denoising methods, the most important statistical models in the fixed basis transform domain are studied. The experimental results are discussed and analyzed to determine the advantages and disadvantages of these methods. The comprehensive study in this paper is a good reference for new research ideas in image denoising.