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Iterative image reconstruction algorithms based on cross-entropy minimization

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1 Author(s)
Byrne, C.L. ; Dept. of Math., Massachusetts Univ., Lowell, MA, USA

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

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Image Processing, IEEE Transactions on  (Volume:2 ,  Issue: 1 )