A Review of Bandlet Methods for Geometrical Image Representation
Mallat, Stéphane; Peyré, Gabriel (2007), A Review of Bandlet Methods for Geometrical Image Representation, Numerical Algorithms, 44, 3, p. 205-234. http://dx.doi.org/10.1007/s11075-007-9092-4
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00359744/en/
Journal nameNumerical Algorithms
MetadataShow full item record
Abstract (EN)This article reviews bandlet approaches to geometric image representations. Orthogonal bandlets using an adaptive segmentation and a local geometric flow well suited to capture the anisotropic regularity of edge structures. They are constructed with a “bandletization” which is a local orthogonal transformation applied to wavelet coefficients. The approximation in these bandlet bases exhibits an asymptotically optimal decay for images that are regular outside a set of regular edges. These bandlets can be used to perform image compression and noise removal. More flexible orthogonal bandlets with less vanishing moments are constructed with orthogonal grouplets that group wavelet coefficients alon a multiscale association field. Applying a translation invariant grouplet transform over a translation invariant wavelet frame leads to state of the art results for image denoising and super-resolution.
Subjects / KeywordsWavelets; Image compression; Image denoising; Super-resolution; Texture synthesis; Orthogonal bandlets
Showing items related by title and author.