Iterative image reconstruction algorithms based on cross-entropy minimization

Author

Byrne, Charles L.

Author_Institution

Dept. of Math., Massachusetts Univ., Lowell, MA, USA

Volume

2

Issue

1

fYear

1993

fDate

1/1/1993 12:00:00 AM

Firstpage

96

Lastpage

103

Abstract

The related problems of minimizing the functionals F(x)=αKL(y,Px)+(1-α)KL(p ,x) and G(x)=αKL(Px,y)+(1-α)KL(x ,p), respectively, over the set of vectors x⩾0 are considered. KL(a, b) is the cross-entropy (or Kullback-Leibler) distance between two nonnegative vectors a and b. Iterative algorithms for minimizing both functionals using the method of alternating projections are derived. A simultaneous version of the multiplicative algebraic reconstruction technique (MART) algorithm, called SMART, is introduced, and its convergence is proved

Keywords

convergence of numerical methods; entropy; functional equations; image reconstruction; iterative methods; Kullback-Leibler distance; SMART; convergence; cross-entropy minimization; functionals; image processing; image reconstruction; iterative algorithms; method of alternating projections; multiplicative algebraic reconstruction technique; nonnegative vectors; Bayesian methods; Cancer; Detectors; Equations; Image reconstruction; Iterative algorithms; Maximum likelihood estimation; Minimization methods; Signal to noise ratio; Tomography;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.210869

Filename

210869