Deformed logarithms. Associated entropic divergences. Applications to linear inverse problems. Inversion algorithms

This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of the considered phenomenon. We will here extend this study to divergence functions based on forms of entropy developed in the field of Statistical Physics. These various forms of entropy are based on "the deformed algebra" [9] and in particularly on the notion of "Deformed Logarithm" [15][9].