Skip to Main content Skip to Navigation
Theses

Méthodes d'approximation pour la reconstruction de signaux et le redimensionnement d'images

Abstract : This work addresses the problems of signal reconstruction and image resizing.
Reconstruction aims at estimating a function given only (eventually noisy) linear measurements performed on it at discrete locations.
For instance, uniform interpolation is the problem of estimating s(t) on the real line, given the values s(k) at the integers k.

The proposed approach is original, and consists in performing a quasi-projection in a given linear shift-invariant reconstruction space, such that the decay of the approximation error is maximal as the sampling step tends to zero.
We illustrate our method in the 1D, 2D Cartesian and 2D hexagonal cases.
We then apply our formalism to the problem of image resizing, for which only non-linear methods are able to correctly synthesize the geometric information to which the human visual system is sensitive.
We propose a method called induction, which is simple, fast and efficient.
Complete list of metadatas

Cited literature [220 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00206144
Contributor : Jean-Michel Vanpé <>
Submitted on : Wednesday, January 16, 2008 - 3:47:08 PM
Last modification on : Friday, November 6, 2020 - 4:12:19 AM
Long-term archiving on: : Tuesday, April 13, 2010 - 9:10:05 PM

Identifiers

  • HAL Id : tel-00206144, version 1

Collections

Citation

Laurent Condat. Méthodes d'approximation pour la reconstruction de signaux et le redimensionnement d'images. Interface homme-machine [cs.HC]. Institut National Polytechnique de Grenoble - INPG, 2006. Français. ⟨tel-00206144⟩

Share

Metrics

Record views

436

Files downloads

4322