Nicholas C. Makris
Naval Res. Lab., Washington, DC 20375
The apparent logarithmic response of human auditory and visual perception to intensity stimulus exhibited is the Weber-Fechner laws is interpreted from the perspective of optimal pattern recognition in signal-dependent noise. The stochastic behavior of acoustic and optical fields received from both fluctuating sources and scatterers can often be well approximated with circular complex Gaussian random (CCGR) variables. Averaged intensity from a CCGR field has a standard deviation proportional to the mean. Therefore, intensity images derived from CCGR fields have signal-dependent noise known as speckle. Taking the logarithm of such intensity images homomorphically transforms the signal-dependent noise into additive signal-independent noise. It has recently been shown that matched filtering such images with hypothetical patterns in the logarithmic domain provides an optimal method for pattern recognition according to the independent perspectives offered by minimum variance unbiased estimation with Fisher information, optimal filtering, and information theory [N. C. Makris, Opt. Lett. (to be published 1995)]. This provides a mathematical justification for the use of logarithmic measurements to efficiently convey information for pattern recognition, and in this context may also provide a basis for the apparent logarithmic response of human auditory and visual perception to intensity stimulus.