The goal of this Thesis is to investigate the mathematical tools and theoretical aspects of the most representative and efficient algorithms in each class of image denoising methods. Basing ourselves on the discovered common features and underlying assumptions we establish a systematisation of modern state-of-the-art algorithms. For each class of algorithms in the Thesis we identify its weaknesses and theoretical limits. The most efficient algorithms have been studied from the point of view of opportunities to serve as a basis for building an universal algorithm for solving the majority of the problems in image processing. In conclusion, in this Thesis, we define the most perspective algorithms for future development, generalisation and extension to image compression, inpainting and restoration.