title: The undecimated wavelet decomposition and its reconstruction.
abstract: This paper describes the undecimated wavelet transform and its reconstruction. In the first part, we show the relation between two well known undecimated wavelet transforms, the standard undecimated wavelet transform and the isotropic undecimated wavelet transform. Then we present new filter banks specially designed for undecimated wavelet decompositions which have some useful properties such as being robust to ringing artifacts which appear generally in wavelet-based denoising methods. A range of examples illustrates the results.
authors.affiliation: CEA-Saclay, DAPNIA/SEDI-SAP, Service d'Astrophysique, F-91191 Gif sur Yvette, France.
authors.forename: Jean-Luc
authors.initials: JL
authors.lastname: Starck
authors.forename: Jalal
authors.initials: J
authors.lastname: Fadili
authors.forename: Fionn
authors.initials: F
authors.lastname: Murtagh
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D012815:Signal Processing, Computer-Assisted