Many inverse problems inherently involve non-linear forward operators. Particular examples include the modelling of the Stejskal-Tanner equation in diffusion tensor imaging, and direct regularisation of the phase of a complex image in MR velocity imaging. The primal-dual algorithm of Chambolle and Pock being advantageous for the numerical solution of non-smooth total variation type regularised optimisation problems, I recently extended it to non-linear operators. In this talk, I will sketch the ingredients for obtaining local convergence, and demonstrate very promising numerical performance.
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