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In this paper we propose a new statistical stopping rule for constrainedmaximum likelihood iterative algorithms applied to ill-posed inverse problems.To this aim we extend the definition of Tikhonov regularization in astatistical framework and prove that the application of the proposed stoppingrule to the Iterative Space Reconstruction Algorithm (ISRA) in the Gaussiancase and Expectation Maximization (EM) in the Poisson case leads to welldefined regularization methods according to the given definition. We also provethat, if an inverse problem is genuinely ill-posed in the sense of Tikhonov,the same definition is not satisfied when ISRA and EM are optimized byclassical stopping rule like Morozov's discrepancy principle, Pearson's testand Poisson discrepancy principle. The stopping rule is illustrated in the caseof image reconstruction from data recorded by the Reuven Ramaty High EnergySolar Spectroscopic Imager (RHESSI). First, by using a simulated imageconsisting of structures analogous to those of a real solar flare we validatethe fidelity and accuracy with which the proposed stopping rule recovers theinput image. Second, the robustness of the method is compared with the otherclassical stopping rules and its advantages are shown in the case of real datarecorded by RHESSI during two different flaring events.

Regularization of constrained maximum likelihood iterative algorithms by means of statistical stopping rule