Energy minimization methods
Résumé
Energy minimization methods are a very popular tool in image and signal processing. This chapter deals with images defined on a discrete finite set. Energy minimization methods are presented from a non classical standpoint: we provide analytical results on their minimizers that reveal salient features of the images recovered in this way, as a function of the shape of the energy itself. The energies under consideration can be differentiable or not, convex or not. Examples and illustrations corroborate the presented results. Applications that take benefit from these results are presented as well.
Mots clés
- Proximal analysis
- Denoising
- Analysis of minimizers
- Variational methods
- Variational methods.
- Total variation
- Stability analysis
- Signal restoration
- Signal and image processing
- Regularization
- Perturbation anal- ysis
- Optimization
- Non-smooth analysis
- Non-convex analysis
- Minimizer function
- Image restora- tion
- Inverse problems
- Edge restoration
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