Image denoising: Learning the noise model via nonsmooth PDE-constrained optimization

Juan Carlos De los Reyes, Carola-Bibiane Schönlieb

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


We propose a nonsmooth PDE-constrained optimization approach for the determination of the correct noise model in total variation (TV) image denoising. An optimization problem for the determination of the weights corresponding to different types of noise distributions is stated and existence of an optimal solution is proved. A tailored regularization approach for the approximation of the optimal parameter values is proposed thereafter and its consistency studied. Additionally, the differentiability of the solution operator is proved and an optimality system characterizing the optimal solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a quasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems. © 2013 American Institute of Mathematical Sciences.
Original languageEnglish (US)
Pages (from-to)1183-1214
Number of pages32
JournalInverse Problems and Imaging
Issue number4
StatePublished - Nov 27 2013
Externally publishedYes


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