Generalization of divergences by application of the deformed logarithm -- Applications to linear inverse problems -- Inversion algorithms

Abstract: The purpose of this note is to extend the divergences analyzed in a previous work by application of the Deformed Logarithm in its most general form. In a study on entropic divergences, we have analyzed the different forms of the deformed logarithm and their applications to this type of divergence. A very general form of the deformed logarithm has been highlighted; it allows us to group the different expressions of the deformed logarithm under a unique form which includes all the others. Beyond the applications linked to the divergences based on entropy, we propose here to extend the classical divergences by application of the generalized deformed Logarithm.