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The aim of this paper is to provide quantitative estimates for the minimizers of non-quadratic regularization problems in terms of the regularization parameter respectively the noise level. As usual for illposed inverse problems, these estimates can be obtained only under additional smoothness assumptions on the data, so-called source conditions, which we identify with the existence of Lagrange multipliers for a limit problem. Under such a source condition, we shall prove a quantitative estimate for the Bregman distance induced by the regularization functional, which turns out to be the natural distance measure to use in this case.
Burger et al. (Tue,) studied this question.