Convex image denoising via non-convex regularization. (English) Zbl 1444.94015
Aujol, Jean-François (ed.) et al., Scale space and variational methods in computer vision. 5th international conference, SSVM 2015, Lège-Cap Ferret, France, May 31 – June 4, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9087, 666-677 (2015).
Summary: Natural image statistics motivate the use of non-convex over convex regularizations for restoring images. However, they are rarely used in practice due to the challenge to find a good minimizer. We propose a Convex Non-Convex (CNC) denoising variational model and an efficient minimization algorithm based on the Alternating Directions Methods of Multipliers (ADMM) approach. We provide theoretical convexity conditions for both the CNC model and the optimization sub-problems arising in the ADMM-based procedure, such that convergence to a unique global minimizer is guaranteed. Numerical examples show that the proposed approach is particularly effective and well suited for images characterized by sparse-gradient distributions.
For the entire collection see [Zbl 1362.68008].
For the entire collection see [Zbl 1362.68008].
MSC:
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 49M25 | Discrete approximations in optimal control |
| 49N45 | Inverse problems in optimal control |
Keywords:
non-convex non-smooth regularization; image denoising; alternating directions method of multipliersReferences:
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