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Pixons and Bayesian image reconstruction
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Paper Abstract

Due to noise processes and resolution limitations, the act of measurement of a particular physical quantity or quantities, Q, leads to a data set which only crudely describes the quantities of interest. Quite naturally, scientists have developed a number of methods which attempt to optimally extract the values, H (or hypothesis), of these underlying quantities from these flawed data sets. This paper describes the theory of the pixon, the fundamental unit of information in a recorded data set. Describing the data in this representation (co-ordinate system of basis) provides an efficient means of extracting the underlying properties. The advantages provided by the pixon description can be understood in terms of Bayesian methods where the pixon basis forms a model with a highly optimized prior. We also show the connection between the pixon concept and Algorithmic Information Content and how pixons can be thought of as a generalization of the Akaike Information Criterion. In addition, the relationship between pixons and 'coarse graining' and the consequences of measurement uncertainty are related to the role of the Heisenberg uncertainty principle in introducing degeneracy in the phase space description of statistical mechanics. Finally, we describe our most current formulation of the Fractal Pixon Basis (FPB) and supply examples of image restoration and reconstruction drawn from the field of astronomical imaging.

Paper Details

Date Published: 30 September 1994
PDF: 20 pages
Proc. SPIE 2302, Image Reconstruction and Restoration, (30 September 1994); doi: 10.1117/12.188069
Show Author Affiliations
Richard Charles Puetter, Univ. of California/San Diego (United States)

Published in SPIE Proceedings Vol. 2302:
Image Reconstruction and Restoration
Timothy J. Schulz; Donald L. Snyder, Editor(s)

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