Energy minimization methods

Mila Nikolova (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

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: Edge restoration; Inverse problems; Image restora- tion; Minimizer function; Non-convex analysis; Non-smooth analysis; Optimization; Perturbation anal- ysis; Proximal analysis; Regularization; Signal and image processing; Signal restoration; Stability analysis; Total variation; Variational methods.; Variational methods; Analysis of minimizers; Denoising

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Mila Nikolova. Energy minimization methods. Otmar SCHERZER. Handbook of Mathematical Methods in Imaging, Springer, pp.138-186, 2011, Springer Reference, 978-0-387-92921-7. ⟨10.1007/978-0-387-92920-0⟩. ⟨hal-00841479⟩