Fisher information for fluctuating intensity and the efficiency of logarithmic measures

Abstract

The optimal resolution of a set of parameters to be estimated from a set of measurements of fluctuating intensity can be determined by computing the respective Fisher information matrix. This matrix is dependent upon the conditional distribution of the fluctuating intensity measurements, given the parameters to be estimated. It is assumed that fluctuating intensity is measured from circular complex Gaussian random (CCGR) fields. Such fields are commonly measured in acoustics, optics, and radar. For example, CCGR fields typically arise in scattering from fluctuating targets and surfaces, random sources, and ocean‐acoustic propagation scintillation. Distributions for intensity, log‐intensity, and acoustic flow (analogous to optical flow) are derived as a function of the measurement‐system averaging time and the temporal coherence of the fluctuating field under the CCGR field assumption. (This advances previous work in ocean‐acoustic propagation scintillation that was limited to instantaneous measurements.) It is shown that the Fisher information for a measurement of fluctuating intensity is expressed in terms of parameter variations over the expectation value of a logarithmic measure of intensity. This gives a mathematical justification for the engineering intuition that fluctuating intensity should be measured in logarithmic units to efficiently convey information. A generalized Fisher information matrix is derived for the estimation of parameters from intensity images.