Abstract

A new solution to the maximum-entropy image-restoration problem, assuming Poisson-noise statistics and multinomial object statistics, is presented. A set of nonlinear equations is solved using Lagrange multipliers in a way analogous to that of Frieden and Wells [ J. Opt. Soc. Am. 68, 93 ( 1978)]. However, unlike the Frieden–Wells solution, the solution presented here is derived without making approximations to the noise statistics. This solution is equivalent to a solution obtained in an earlier paper using recursive methods [ J. Opt. Soc. Am. A 76, 787 ( 1986)]. The simplicity of the recursive solution permits an interpretation that shows how the maximum-entropy method arrives at a maximally smooth solution.

© 1988 Optical Society of America

Maximum entropy image restoration. I. The entropy expression

Ryoichi Kikuchi and B. H. Soffer
J. Opt. Soc. Am. 67(12) 1656-1665 (1977)

Restoring with maximum entropy. III. Poisson sources and backgrounds

B. Roy Frieden and Donald C. Wells
J. Opt. Soc. Am. 68(1) 93-103 (1978)

Origins of linear and nonlinear recursive restoration algorithms

Edward S. Meinel
J. Opt. Soc. Am. A 3(6) 787-799 (1986)

Restoring with Maximum Likelihood and Maximum Entropy*

B. Roy Frieden
J. Opt. Soc. Am. 62(4) 511-518 (1972)

Maximum entropy method for diffractive imaging

Hiroyuki Shioya and Kazutoshi Gohara
J. Opt. Soc. Am. A 25(11) 2846-2850 (2008)