Article deals with synthesis and analysis of detector of fractal signal at the background of non-correlated Gaussian noise. Model of signal is fractional Brownian motion (fBm), which describes many types of signal particularly flicker-noise. Expression for likelihood ratio is given being based on fBm models in time and spectral fields. This expression is a sufficient statistics for many problems of signal processing. Detection characteristics of fBm are calculated by analytical method and statistical simulation. Investigation results are distributed on image processing in terms of usage fractional Brownian surface (fBs) model.