A study of the relationships between the real scene statistics and those of the backscattered signal

Popular mathematical description of natural landscapes rely upon fractal geometry and a peculiar parameter of the model is the Hurst coefficient HX , which rules the correlation properties of the real scene. The random process modelling the remotely collected data may preserve the fractal behavior of the original scene and its second-order statistics is then characterized by a Hurst number HY . However, HY = HX is only one of the possibilities arising from the mapping real scene → collected data. The relationships between the two Hurst parameters, hence between the second-order properties of the correspondent random processes, are investigated in the simplified scenario where the above mapping is a zeromemory nonlinearity. The obtained results improve and corroborate the work of [2].

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