Fractal approach to mathematical modelling of signals in space optical observation systems is proposed. The scannings of two-dimensional images as one-dimensional stochastic fractal processes are built on the base of Brownian motion. Integrals over trajectories of Wiener processes with different kernels are used for modeling of one-dimensional stochastic fractals and multifractals. Modelling of scannings of remotely sensed data based on formalism of integrals over Wiener stochastic process trajectories and modelling of probabilistic characteristics based on formalism of Feynman continual integrals are performed. Algorithms of multiscale detection of signals on the basis of discrete and continuous wavelet transforms are developed and applied for anomaly detection and estimation.