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Journal Articles Computer Vision and Image Understanding Year : 2009

Manifold Models for Signals and Images


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.
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hal-00359729 , version 1 (09-02-2009)


  • HAL Id : hal-00359729 , version 1


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