Manifold models for signals and images

  • Authors:
  • Gabriel Peyré

  • Affiliations:
  • CNRS and CEREMADE, Université Paris-Dauphine, Place du Maréchal De Lattre, De Tassigny, 75775 Paris Cedex 16, France

  • Venue:
  • Computer Vision and Image Understanding
  • Year:
  • 2009

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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.