Manifold Models for Signals and Images

Gabriel Peyré (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

This article proposes a new class of models for natural signals and images. These models constrain the set of patches extracted from the data to analyze to be close to a low dimensional manifold. This manifold structure is detailed for various ensembles suitable for natural signals, images and textures modeling. These manifolds provide a low-dimensional parameterization of the local geometry of these datasets. These manifold models can be used to regularize inverse problems in signal and image processing. The restored signal is represented as a smooth curve or surface traced on the manifold that matches the forward measurements. A manifold pursuit algorithm computes iteratively a solution of the manifold regularization problem. Numerical simulations on inpainting and compressive sensing inversion show that manifolds models bring an improvement for the recovery of data with geometrical features.

Mots clés: manifold; signal processing; image modeling; texture; manifold.

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

Gabriel Peyré. Manifold Models for Signals and Images. Computer Vision and Image Understanding, 2009, 113 (2), pp.249-260. ⟨hal-00359729⟩