Pixon‐based multiresolution image reconstruction and the quantification of picture information content

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Abstract
This article reviews pixon‐based image reconstruction, which in its current formulation uses a multiresolution language to quantify an image's algorithmic information content (AIC) using Bayesian techniques. Each pixon (or its generalization, theinformation) represents a fundamental quanta of an image's AIC, and an image's pixon basis represents the minimum degrees of freedom necessary to describe the image within the 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 maximum entropy methods. Typical improvements include higher spatial resolution, greater sensitivity to faint sources, and immunity to the production of spurious sources and signal correlated residuals. Finally, we show how the pixon provides a generalization of the Akaike information criterion, and how it relates to concepts of “coarse graining” and the role of the Heisenberg uncertainly principle in statistical mechanics, provides a mechanism for optimal data compression, and represents a more optimal basis for image compression or reconstruction than wavelets.

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