The entropic prior for distributions with positive and negative values (original) (raw)

Journal Article

M. P. Hobson ,

Mullard Radio Astronomy Observatory, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE

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A. N. Lasenby

Mullard Radio Astronomy Observatory, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE

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Published:

11 August 1998

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Abstract

The maximum entropy method has been used to reconstruct images in a wide range of astronomical fields, but in its traditional form it is restricted to the reconstruction of strictly positive distributions. We present an extension of the standard method to include distributions that can take both positive and negative values. The method may therefore be applied to a much wider range of astronomical reconstruction problems. In particular, we derive the form of the entropy for positive/negative distributions and use direct counting arguments to find the form of the entropic prior. We also derive the measure on the space of positive/negative distributions, which allows the definition of probability integrals and hence the proper quantification of errors.

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© 1998 RAS