The signature that a remotely sensed scene imprints on the backscattered signal

A self-similar natural scene, characterized by a Hurst coefficient H_X>1/2, is remotely sensed. The physical process of data acquisition is modeled as a non-linear zero-memory function of the natural scene slope. Do the data collected by the sensor preserve the long-range-dependence feature? If they do, what about the relationship between the Hurst coefficient of the illuminated scene and that of the collected data? This is our first investigation of the issue; as such, we resort to an extremely simplified setup allowing us to highlight some interesting problem features