Parameter estimation bounds for acoustic intensity images

Abstract

A generalized Cramer–Rao lower bound is derived for the estimation of parameters from intensity images. It is assumed that the intensity assigned to each pixel value in an image is measured from a circular complex Gaussian random (CCGR) field. Such fields are commonly measured in acoustics, optics, and radar. However, intensity images obtained from acoustic measurements generally have lower SNR than in optics or microwave radar, making parameter estimation more difficult. This is because acoustic coherence time scales are generally much larger than those in optics or microwave radar relative to the respective stationary time scales. Therefore, it is especially important to determine the practicality of the parameter estimate by determining the optimal resolution attainable. Various analytic bounds are derived including those for estimation of scattering strength, transmission loss, the orientation of a Lambertian surface by stereoscopic analysis, the location and recognition of an object, the resolution of blurred features in a set of images, and the motion or acoustic flow (analogous to optical flow) of an object over a series of blurred images. The applications presented are for underwater imaging systems, but the formulation is generally applicable to arbitrary beamformed imaging of CCGR fields. This work is directly applicable to pattern recognition.