E.A. Semenishchev, I.S. Shraifel, V.I. Marchuk, I.A. Toropov

The development and widespread adoption of digital communication systems, the use of new light-sensitive matrices, as well as the creation of automated control systems with cameras, make an urgent task denoising of the action in images. The main causes of the noise component in the digital image can be considered: the lack of illumination of the subject, a limited number of active light-sensitive elements, a linear or inaccurate gamma correction, inhomogeneity of the crystal lattice and the impurities in it; noise analog electronics (analog-digital conversion, noise amplifiers, light-sensitive binding matrix), etc. The presence of noise in the image, making it difficult to perception. The most noticeable is the noise component in the plain areas of the image. Preserving boundaries for image filtering is also an important task. In this connection, the simultaneous reduction of the noise component of the image while preserving the boundaries of objects and highly detailed parts in a limited amount of a priori information about the useful and noise components is an important task. In the paper a multi-criteria method for smoothing two-dimensional digital signals. Studies have shown that the estimates obtained in the processing of the target function has an extremum, prove its strict convexity. Expressions are given for finding the smoothed values of the two-dimensional digital signal by the proposed method.