Maximum Entropy Image Estimation Analysis of image Formation with Thinned Random Arrays.

Abstract

Abstract : Two related topics were studied in this three-year research program. The first was imaging behavior of thinned, or sparse arrays of small antennas, or apertures whatever the wavelength may be. The radiation properties of these arrays are known. We have made the first study of their imaging quality using computer simulation for coherent, partially coherent and incoherent radiation. Varying conditions of signal to noise, phase aberration and monochromaticity were studied. For incoherent light, thinning down to 6% of the full aperture produced no noticeable degradation. The arrays are easy to design and degrade gracefullly when large fractions of the elements fail. The result of this study can be found in the Interim Scientific Report. The second topic studied, the one discussed in this report, was the maximum entropy (ME) image reconstruction method. We formulate the problem from a fundamental point of view based on the physical statistics of the problem. The most probable object consistent with the measured signal image data and the noise is selected as the estimated object. The entropy is the logarithm of the probability. The constrained entropy is analogous, we note, to the free energy of statistical mechanics and we utilize this analogy to consider the problem of fluctuations, or noise in a natural way. The degree of confidence in the ME estimate is derived in a general manner by expanding the object probability distribution near the maximum as a multivariate Gaussian and making a principal axis transformation.