Morozov principle for Kullback-Leibler residual term and Poisson noise

Bruno Sixou (1) , Tom Hohweiller (1) , Nicolas Ducros (1)

1 Imagerie Tomographique et Radiothérapie

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.

Mots clés: Morozov principle; Inverse problems; Kullback-Leibler divergence

Domaines: Imagerie médicale; Traitement du signal et de l'image [eess.SP]

Bruno Sixou, Tom Hohweiller, Nicolas Ducros. Morozov principle for Kullback-Leibler residual term and Poisson noise. Inverse Problems and Imaging , 2018, 12 (3), pp.607 - 634. ⟨10.3934/ipi.2018026⟩. ⟨hal-01880210⟩