Iterative image reconstruction algorithms based on cross-entropy minimization.

The related problems of minimizing the functionals F(x)=alphaKL(y,Px)+(1-alpha)KL(p,x) and G(x)=alphaKL(Px,y)+(1-alpha)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.