Contents I. Introduction
In radar imagery, the observed intensity is the sum of the contributions of the different scatterers at the observed surface. In the classical approach, the number of scatterers in each elementary cell is assumed to be large enough and approximately constant. The reflected electrical field is then Gaussian; the observed intensity admits an exponential distribution, and the amplitude admits a Rayleigh one. However, when the number of scatterers varies, the distribution of the resulting field may be non-Gaussian, and so the observed intensity may no longer be exponential. Assuming that the random number of scatterers in each elementary cell is distributed according to a Poisson distribution, one can consider that the mean of this distribution, or the “expected number of scatterers,” is itself a random variable [14]. It is well known that when this random variable is Gamma distributed, the intensity of the back-scattered field is distributed [2]–[7], [12]–[15], [17], [20], [22], [27]. In this paper, we extend the possibilities of distributions of this expected number of scatterers to three new distributions—inverse Gamma, Beta of the first kind, or Beta of the second kind—and show that the intensity distribution of the back-scattered field can be calculated in these three new cases. Furthermore, we propose a method of classification, using only the observed image, in which case, among four possibilities including the classical case and the three new cases, the observed intensity data lie. The usefulness of the three new distributions is tested on a real image, and it turns out that there exist situations in which the new distributions are of interest.
