Convex Inverse Scale Spaces

Inverse scale space methods are derived as asymptotic limits of iterative regularization methods. They have proven to be efficient methods for denoising of gray valued images and for the evaluation of unbounded operators. In the beginning, inverse scale space methods have been derived from iterative regularization methods with squared Hilbert norm regularization terms, and later this concept was generalized to Bregman distance regularization (replacing the squared regularization norms); therefore allowing for instance to consider iterative total variation regularization. We have proven recently existence of a solution of the associated inverse total variation flow equation. In this paper we generalize these results and prove existence of solutions of inverse flow equations derived from iterative regularization with general convex regularization functionals. We present some applications to filtering of color data and for the stable evaluation of the DiZenzo edge detector.