Maximum entropy methods in coherent radar imaging

Abstract

AbstractThere are some compelling reasons for viewing the problem of image reconstruction from noisy or incomplete data as one of statistical estimation, i.e., of choosing, from the infinity of images consistent with the data, that image which, in some statistical sense, is most plausible. Among these reasons are the soundness of the philosophical underpinning of the resulting image reconstruction process, a greater realization of the image resolution which is inherent in the data, and freedom from many of the artifacts encountered in commonly used ad hoc reconstruction schemes. One successful technique employing a principle of statistical inference is the maximum entropy technique, in which the data‐consistent image with maximum configurational entropy is chosen. It is a computationally intensive approach involving a conjugate gradient search over a convex function of a vector in a space of dimensionality equal to the number of image pixels. This technique has been employed with success in situations where the data samples are modeled as linearly related to a real non‐negative object. We investigate application of maximum entropy image reconstruction to the problem of high‐resolution radar diagnostic imaging. The problem differs from others in which maximum entropy has been applied in that the object to be imaged is complex. Although the desired image is of the magnitude of the complex object and is thus real and non‐negative, there is no linear relationship beween object magnitude and data. Rather, the data are linearly related to the complex object. Several earlier proposed methods for applying the maximum entropy principle to this problem are identified and analyzed. A method that more closely approximates true Bayesian estimation is proposed.