Manifold Models for Signals and Images
Peyré, Gabriel (2009), Manifold Models for Signals and Images, Computer Vision and Image Understanding, 113, 2, p. 249-260. http://dx.doi.org/10.1016/j.cviu.2008.09.003
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00359729/en/
Journal nameComputer Vision and Image Understanding
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Abstract (EN)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.
Subjects / Keywordssignal processing
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