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Reconstruction of Binary Images via the EM Algorithm

  • Yehuda Vardi
  • Cun-Hui Zhang
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

The problem of reconstructing a binary function x defined on a finite subset of a lattice ℤ, from an arbitrary collection of its partial sums is considered. The approach is based on (a) relaxing the binary constraints \(x\left( i \right) = 0\) or 1 to interval constraints \(0x\left( i \right)1,i \in {\Bbb Z}\),and (b) applying a minimum distance method (using Kullback-Leibler’s information divergence index as our distance function) to find such an x — say, \(\hat x\)— for which the distance between the observed and the theoretical partial sums is as small as possible (Turning this \(\hat x\) into a binary function can be done as a separate postprocessing step: for instance,through thresholding, or through some additional Bayes modeling.) This minimum-distance solution is derived via a new EM algorithm that extends the often-studied EM/maximum likelihood (EM/ML) algorithm in emission tomography and certain linear-inverse problems to include lower-and upper-bound constraints on the function x. Properties of the algorithm including convergence and uniqueness conditions on the solution (or parts of it) are described.

Keywords

Binary Image Maximum Likelihood Estimator Probability Vector Binary Function Binary Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Yehuda Vardi
    • 1
  • Cun-Hui Zhang
    • 1
  1. 1.Department of StatisticsRutgers UniversityPiscatawayUSA

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