Maximum-likelihood constrained regularized algorithms: an objective criterion for the determination of regularization parameters

Henri Lanteri; Muriel Roche; Olga Cuevas; Claude Aime

doi:10.1117/12.371319

10 December 1999 Maximum-likelihood constrained regularized algorithms: an objective criterion for the determination of regularization parameters

Henri Lanteri, Muriel Roche, Olga Cuevas, Claude Aime

Author Affiliations +

Proceedings Volume 3866, Optics in Atmospheric Propagation and Adaptive Systems III; (1999) https://doi.org/10.1117/12.371319
Event: Remote Sensing, 1999, Florence, Italy

Abstract

We propose regularized versions of Maximum Likelihood algorithms for Poisson process with non-negativity constraint. For such process, the best-known (non- regularized) algorithm is that of Richardson-Lucy, extensively used for astronomical applications. Regularization is necessary to prevent an amplification of the noise during the iterative reconstruction; this can be done either by limiting the iteration number or by introducing a penalty term. In this Communication, we focus our attention on the explicit regularization using Tikhonov (Identity and Laplacian operator) or entropy terms (Kullback-Leibler and Csiszar divergences). The algorithms are established from the Kuhn-Tucker first order optimality conditions for the minimization of the Lagrange function and from the method of successive substitutions. The algorithms may be written in a `product form'. Numerical illustrations are given for simulated images corrupted by photon noise. The effects of the regularization are shown in the Fourier plane. The tests we have made indicate that a noticeable improvement of the results may be obtained for some of these explicitly regularized algorithms. We also show that a comparison with a Wiener filter can give the optimal regularizing conditions (operator and strength).

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Henri Lanteri, Muriel Roche, Olga Cuevas, and Claude Aime "Maximum-likelihood constrained regularized algorithms: an objective criterion for the determination of regularization parameters", Proc. SPIE 3866, Optics in Atmospheric Propagation and Adaptive Systems III, (10 December 1999); https://doi.org/10.1117/12.371319

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