It is well known that interactions between a coherent monochromatic radiation and a scattering media induce a speckle phenomenon. Spatial and temporal statistics of this speckle allow many applications in laser imaging. The main problem is the characterization of the backscattered media from the speckle pattern in biomedical imagery. In this paper, we present a stochastic approach based on Brownian motion theory in the approximation of the diffusion. Stochastic processes showing statistical scale law are, under some assumptions, called fractional Brownian motion (fBm) which is a generalization of ordinary Brownian motion (Bm) as defined by Mandelbrot and Van Ness. This extension is related to the existence of a long-range statistic dependence in the process. This dependence is quantified by the Hurst exponent H that is a 'scale factor' indicating the persistence (H>0.5), totally random (H=0.5) or the anti-persistence (H<0.5) nature of the process. Variogram analysis is a possible method to estimate the Hurst exponent. We applied this approach by estimation of the mean quadratic spatial difference, or diffusion function, for 2D analysis of speckle image. Hence, spatial speckle is characterize by extracting from diffusion function plot a set of three parameters; the Hurst exponent, the saturation of the variance and the characteristic element size. Applications of this method to characterization of test media are presented. We find that for all test media with different latex micro-ball concentrations (1%, 5% and 10%) the characteristic element size and the saturation of the variance discriminate media while Hurst exponent seems to be constant for all concentrations. This first results permit us to hope in application like skin lesion quantification in dermatology.