Continuous Wavelet Decompositions, Multiresolution, and Contrast Analysis

International audienceA continuous version of multiresolution analysis is described, starting from usual continuous wavelet decompositions. Scale discretization leads to decompositions into functions of arbitrary bandwidth, satisfying QMF-like conditions. Finally, a nonlinear multiresolution scheme is described, providing multiplicative reconstruction formulas

Exact reconstruction with directional wavelets on the sphere

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux et al. (2005). The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation is firstly identified. A scale discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background (CMB) data, such as the imprint of topological defects, in particular cosmic strings, and for their reconstruction after separation from the other signal components.Comment: 22 pages, 2 figures. Version 2 matches version accepted for publication in MNRAS. Version 3 (identical to version 2) posted for code release announcement - "Steerable scale discretised wavelets on the sphere" - S2DW code available for download at http://www.mrao.cam.ac.uk/~jdm57/software.htm

Recherches immunologiques sur les lactoglobulines anticorps de virus

Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

La fonction de sensibilite aux contrastes sous stimulation vestibulaire

SIGLECNRS RP 174 (223) / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Systeme d'evaluation de la vision fonctionnelle et de depistage de la basse vision

Available at INIST (FR), Document Supply Service, under shelf-number : RP 10395 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

Influence de frequences spatiales sur l'extraction de cibles

SIGLECNRS RP 174 (216) / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc