PIXON-BASED MULTIRESOLUTION IMAGE-RECONSTRUCTION AND THE QUANTIFICATION OF PICTURE INFORMATION-CONTENT

This article reviews pixon-based image reconstruction, which in its cu rrent formulation uses a multiresolution language to quantify an image 's algorithmic information content (AIC) using Bayesian techniques. Ea ch pixon (or its generalization, the informaton) represents a fundamen tal quanta of an image's AlC, and an image's pixon basis represents th e minimum degrees of freedom necessary to describe the image within th e accuracy of the noise. We demonstrate with a number of examples that pixon-based image reconstruction yields results consistently superior to popular competing methods, including maximum likelihood and maximu m entropy methods. Typical improvements include higher spatial resolut ion, greater sensitivity to faint sources, and immunity to the product ion of spurious sources and signal correlated residuals. Finally, we s how how the pixon provides a generalization of the Akaike information criterion, and how it relates to concepts of ''coarse graining'' and t he role of the Heisenberg uncertainty principle in statistical mechani cs, provides a mechanism for optimal data compression, and represents a more optimal basis for image compression or reconstruction than wave lets. (C) 1995 John Wiley & Sons, Inc.