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June  2018, 12(3): 607-634. doi: 10.3934/ipi.2018026

## Morozov principle for Kullback-Leibler residual term and Poisson noise

 CREATIS, CNRS UMR 5220, INSERM U1044, INSA de Lyon, Université de Lyon 1, Université de Lyon, 69621, Villeurbanne Cedex, France

Received  June 2017 Revised  November 2017 Published  March 2018

We study the properties of a regularization method for inverse problems corrupted by Poisson noise with Kullback-Leibler divergence as data term. The regularization parameter is chosen according to a Morozov type principle. We show that this method of choice of the parameter is well-defined. This a posteriori choice leads to a convergent regularization method. Convergences rates are obtained for this a posteriori choice of the regularization parameter when some source condition is satisfied.

Citation: Bruno Sixou, Tom Hohweiller, Nicolas Ducros. Morozov principle for Kullback-Leibler residual term and Poisson noise. Inverse Problems & Imaging, 2018, 12 (3) : 607-634. doi: 10.3934/ipi.2018026
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##### References:
Evolution of the Kullback-Leibler functional for $I = 3$ and $P = 6820$. The value $m/2$ is displayed for comparison
Maps of the reconstructed bone and soft tissues projected mass for $I = 3$ and $P = 6820$
Evolution of the Kullback-Leibler functional for $I = 10$ and $P = 1737984$.The value $m/2$ is displayed for comparison
Maps of the reconstructed bone and soft tissues projected mass for $I = 10$ and $P = 1737984$
Evolution of the Kullback-Leibler functional for $I = 3$ and $P = 108624$. The value $m/2$ is displayed for comparison
Maps of the reconstructed bone and soft tissues projected mass for $I = 3$ and $P = 108624$
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