Regularization of multiplicative iterative algorithms with non-negative constraint

This paper studies the regularization of constrained Maximum Likelihood iterative algorithms applied to incompatible ill-posed linear inverse problems. Specifically we introduce a novel stopping rule which defines a regularization algorithm for the Iterative Space Reconstruction Algorithm in the case of Least-Squares minimization. Further we show that the same rule regularizes the Expectation Maximization algorithm in the case of Kullback-Leibler minimization provided a well- justified modification of the definition of Tikhonov regularization is introduced. The performances of this stopping rule are illustrated in the case of an image reconstruction problem in X-ray solar astronomy