A class of nonlinear diffusion equations with a power-law dependence of the coefficient on the gradient is considered. Such equations are used in the problem of suppressing image noise. The mathematical properties of this class of equations are considered. One of them ensures protection of image edges. Computational results on noise elimination in real-life images are presented. The book is intended for scientists and engineers working in mathematical physics, differential equations, and image processing and for college and university professors and postgraduate and graduate students.