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.
Author(s): Mallat S., Peyré G.
Year: 2007
Language: English
Pages: 30
Geometry of images and textures......Page 1
1D wavelets bases......Page 4
2D wavelet bases......Page 5
Geometric representations of images......Page 8
Finite elements......Page 9
Curvelets......Page 10
Orthogonal bandlets......Page 11
Regularity of wavelet coefficients......Page 12
Polynomial approximation of wavelets coefficients......Page 13
Orthogonal bandlets approximation......Page 14
Applications of orthogonal bandlets......Page 17
Grouping bandlets......Page 20
Orthogonal grouplets......Page 21
Translation invariant grouplet tight frame......Page 24
From grouplets to bandlets......Page 25
Applications of grouplets......Page 26
References......Page 29
