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1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Abstract : 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.

Keywords : manifold signal processing image modeling texture manifold.





Author: Gabriel Peyré -

Source: https://hal.archives-ouvertes.fr/



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