Reconstruction of complex signals using minimum Rényi information

An information divergence, such as Shannon mutual information, measures the distance between two probability-density functions (or images). A wide class of such measures, called α divergences, with desirable properties such as convexity over all space, was defined by Amari. Rényi's information Dα is an α divergence. Because of its convexity property, the minimum of Dα is easily attained. Minimization accomplishes minimum distance (maximum resemblance) between an unknown image and a known reference image. Such a biasing effect permits complex images, such as occur in inverse syntheticaperture- radar imaging, to be well reconstructed. The algorithm permits complex amplitudes to replace the probabilities in the Rényi form. The bias image may be constructed as a smooth version of the linear, Fourier reconstruction of the data. Examples on simulated complex image data with and without noise indicate that the Rényi reconstruction approach permits superresolution in low-noise cases and higher fidelity than ordinary, linear reconstructions in higher-noise cases.