Image denoising: learning the noise model via nonsmooth PDE-constrained optimization. (English) Zbl 1283.49005
Summary: 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 is 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.
MSC:
49M15 | Newton-type methods |
94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
68U10 | Computing methodologies for image processing |
65K10 | Numerical optimization and variational techniques |
90C53 | Methods of quasi-Newton type |