Iterative image reconstruction algorithms based on cross-entropy minimization

The related problems of minimizing the functionals F(x)= alpha KL(y,Px)+(1- alpha )KL(p,x) and G(x)= alpha KL(Px,y)+(1- alpha )KL(x,p), respectively, over the set of vectors x>or=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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