Image recovery from correlations

Abstract

Many image-recovery problems involve the determination of a real-valued, nonnegative image whose nth-order correlation approximates some measured or specified function. Special cases are image recovery from second-order correlations, or phase retrieval, and image recovery from third-order correlations, or triple-correlation recovery. Examples include astronomical speckle imaging, spectroscopy, imaging correlography, and the measurement of ultrashort laser pulses. We propose an iterative technique for recovering images from measurements of nth-order correlations. This technique is shown to preserve nonnegativity, allow for the inclusion of known support constraints, and produce a sequence of images whose nth-order correlations better approximate the measured data as the iterations proceed.