COMPARISON OF GAUSSIAN AND RAYLEIGH NOISE MODELS IN INVERSION OF SUBSURFACE PARAMETERS OF LAYERED ROUGH SURFACES USING SIMULATED ANNEALING Alireza Tabatabaeenejad and Mahta Moghaddam Radiation Laboratory Department of Electrical Engineering and Computer Science University of Michigan 1301 Beal Avenue, Ann Arbor, MI 48109 1. INTRODUCTION The problem of determining the subsurface properties of layered rough surface structures—representative models for soil, rivers, and lakes—from scattering data arises in many areas of science and engineering. It has been shown that Simulated Annealing is a powerful tool for inversion of the model parameters of these structures [1]. The sensitivity of the Simulated Annealing method to measurement noise has also been investigated assuming Gaussian noise contaminates the measured scattering coefficient, or measured scattered power [1]. While the analysis based on this noise model offers insight into the sensitivity of the inversion algorithm to measured data that deviate from what commonly-used forward models predict, it is more appropriate to consider that Gaussian noise perturbs the measured scattered field. This assumption is shown to be equivalent to assuming the scattered power being contaminated by noise with a Rayleigh distribution. The results of the new noise analysis, presented in this work, are expected to be more consistent with inversion results when real data are used. 2. NOISE MODELS We can consider two different noise models in investigating the performance of an inverse scattering problem associated with rough surfaces. One choice is to assume the measured bistatic scattering coefficient is directly contaminated by Gaussian noise as in γ o n = γ o syn + N (0,σ 2 ) (1) where γ o n denotes the measured bistatic scattering coefficient and γ o syn denotes the synthesized noise-free bistatic scattering coefficient. In this work, we use Small Perturbation Method (SPM) to synthesize data [2]. The quantity N (0,σ 2 ) represents the measurement noise, which is assumed to have a Gaussian distribution with a zero mean and a standard deviation of σ. We assume that the standard deviation of the measurement noise is directly proportional to the strength of the signal, i.e., σ =Δγ o syn . Since N (0,σ 2 )= σN (0, 1) = Δγ o syn N (0, 1), γ o n = γ o syn +Δγ o syn N (0, 1) (2) We may use another noise model in which the Gaussian noise contaminates the received electric field. Assume v n = v + N (0,σ 2 ) (3) where v denotes the noise free voltage and v n denotes the measured voltage received at the antenna. Assuming σ =Δv, we have v 2 n = v 2 +2vΔN (0, 1) + Δ 2 v 2 N (0, 1) 2 (4) Averaging (4) over realizations of the rough surface with the assumption that N (0, 1) and v are independent random variables, v 2 n  = v 2  +Δ 2 v 2 N (0, 1) 2 (5) Since the measured voltage is proportional to the measured electric field, γ o n = γ o syn +Δ 2 γ o syn N (0, 1) 2 (6) where N (0, 1) 2 has a Rayleigh distribution.