The relationship between image restoration by the maximum a posteriori method and a maximum entropy method

Abstract

For the linear imaging model g = Hf + n, the maximum a posteriori (MAP) restoration method is compared to the maximum entropy (ME) method defined by maximizing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f_{T} \ln f</tex> subject to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\parallelg - Hf\parallel^{2} = \paralleln\parallel^{2}</tex> . It is shown that the ME solution is a member of the set of MAP solutions defined by a set of a priori probability densities. The numerical methods developed for MAP restoration can be applied to ME restoration. The importance of the a priori probability distribution for the MAP restoration is demonstrated. Examples of ME restoration with the new method are shown and compared to previous results.