Optimally resolving Lambertian surface orientation

Abstract

Sonar images of remote surfaces are typically corrupted by signal-dependent noise known as speckle. Relative motion between source, surface, and receiver causes the received field to fluctuate over time with circular complex Gaussian random (CCGR) statistics. In many cases of practical importance, Lambert’s law is appropriate to model radiant intensity from the surface. In a previous paper, maximum likelihood estimators (MLE) for Lambertian surface orientation have been derived based on CCGR measurements [N. C. Makris, SACLANT Conference Proceedings Series CP-45, 1997, pp. 339–346]. A Lambertian surface needs to be observed from more than one illumination direction for its orientation to be properly constrained. It is found, however, that MLE performance varies significantly with illumination direction due to the inherently nonlinear nature of this problem. It is shown that a large number of samples is often required to optimally resolve surface orientation using the optimality criteria of the MLE derived in Naftali and Makris [J. Acoust. Soc. Am. 110, 1917–1930 (2001)].