Abstract

The two entropy expressions, log<i>B</i> and – <i>B</i> log<i>B</i> (where <i>B</i> is the local brightness of the object or its spatial spectral power) used in maximum entropy (ME) image restoration, are derived as limiting cases of a general entropy formula. The brightness <i>B</i> is represented by the <i>n</i> photons emitted from a small unit area of the object and imaged in the receiver. These <i>n</i> photons can be distributed over <i>z</i> degrees of freedom in <i>q</i>(<i>n</i>,<i>z</i>) different ways calculated by the Bose-Einstein statistics. The entropy to be maximized is interpreted, as in the original definition of entropy by Boltzmann and Planck, as log<i>q</i>(<i>n</i>,<i>z</i>). This entropy expression reduces to log<i>B</i> and – <i>B</i> log<i>B</i> in the limits of <i>n</i> ≫ <i>z</i> > 1 and <i>n</i> ≪ <i>z</i>, respectively. When <i>n</i> is interpreted as an average n¯ over an ensemble, the above two criteria remain the same (with <i>n</i> replaced by n¯), and in addition for the <i>z</i> = 1 case the log<i>B</i> expression, used in ME spectral power estimation, is derived for n¯ ≫ <i>z</i> = 1.

© 1978 Optical Society of America

PDF Article

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription