Optimal Signal and Image Processing in Presence of Additive Fractal Interference

The article deals with algorithms for signal and image processing in presence of interference from the underlying surface, flicker noise, and other types of interference with fractal properties. Models of fractal interference are considered on the basis of the statistical approach. Application of the fractal Brownian motion model with fractional dimension is proved for the statistical description of low-frequency flicker noise is proved, and, also, for describing the reflection coefficient of the sensing signal from the background of natural origin under obtaining the radar images. A maximum likelihood algorithm for detecting signals and extended objects, as well at the background of additive fractal noise are developed. The characteristics of detection of extended objects at the background of fractal noise, as well as a low-frequency signal at the background of flicker noise are calculated. The statistical modeling of the object detection algorithm on raster and complex images of the earth’s surface was carried out and its efficiency was evaluated. It is established that usage of the fractal models allows improving the efficiency of signal and image processing at the background of noise in cases where there are no other differences between them.