Regularization of multiplicative iterative algorithms with nonnegative constraint

This paper studies the regularization of the 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 the x-ray solar astronomy.