Observability of the Scattering Cross-section for Strong and Weak Scattering - Fayard, Patrick (My University, 2010)
Jakeman's random walk model with step number fluctuations describes the amplitude scattered from a rough medium in terms as the coherent summation of (independent) individual scatterers' contributions. For a population following a birthdeath- immigration (BDI) model, the resulting statistics are k-distributed and the multiplicative representation of the amplitude as a Gaussian speckle modulated by a Gamma radar cross-section (RCS) is recovered. The main objective of the present thesis is to discuss techniques for the inference of the RCS in local time in order to facilitate anomaly detection. We first show how the Pearson class of diffusions, which we derive on the basis of a discrete population model analogous to the BDI, encompasses this Gamma texture as well as other texture models studied in the literature. Next we recall how Field & Tough derived, in an Ito calculus framework, the dynamics and the auto-correlation function of the scattered amplitude from the random walk model. In particular, they showed how the RCS was observable through the intensity-weighted squared fluctuations of the phase. Thanks to a discussion of the sources of discrepancy arising during this process, we derive an analytical expression for the inference error based on its asymptotic behaviours, together with a condition to minimize it. Our results are then extended to the Pearson class of diffusions whose importance for radar clutters is described. Next, we consider an experimental caveat, namely the presence of an additional white noise. The finite impulse response Wiener filter enables the design of the optimal filter to retrieve the scattered amplitude when it lies in superposition with thermal noise, thus enabling the usage of our inference technique. Finally, we consider weak scattering when a coherent signal lies in superposition with the aforementioned (strongly) scattered amplitude. Strong and weak scattering patterns differ regarding the correlation structure of their radial and angular fluctuations. Investigating these geometric characteristics yields two distinct procedures to infer the scattering cross-section from the phase and intensity fluctuations of the weakly scattered amplitude, thus generalizing the results obtained in the strong scattering case.
Keywords: sacttering; coherent summation; birth-death-immigration; anomaly detection