Abstract:
Sonar images of remote surfaces are typically corrupted by signal-dependent noise known as speckle. This noise arises when wavelength scale roughness on the surface causes a random interference pattern in the sound field scattered from it by an active system. Relative motion between source, surface, and receiver cause the received field to fluctuate over time with complex Gaussian statistics. Underlying these fluctuations, however, is the expected radiant intensity from the surface, from which its orientation may be inferred. In many cases of practical importance, Lambert's law is appropriate for such inference because variations in the projected area of a surface patch, as a function of source and receiver orientation, often cause the predominant variations in its radiance. Therefore, maximum likelihood estimators for Lambertian surface orientation are derived. These are asymptotically optimal when a sufficiently large number of independent samples are available, even though the relationship between surface orientation and measured radiance is generally nonlinear. Here, the term optimal means that the estimate is unbiased and its mean square error equals the Cramer--Rao lower bound, which is also derived. The requisite number of independent samples necessary for asymptotic optimality of the maximum likelihood estimate is given for some special cases.