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Continuous Wavelet Transform on the Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid

H_+^2

. First, we define a class of suitable dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO ...

2007

Space-frequency quantization for image compression with directionlets

Martin Vetterli, Vladan Velisavljevic

The standard separable 2-D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1-D discontinuities, like edges or contours. ...

2007

Generalized Daubechies Wavelet Families

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9⁄7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynom ...

IEEE2007

Image Coding of 3D Volume Using Wavelet Transform for Fast Retrieval of 2D Images

Vijayaraghavan Thirumalai

An encoder/decoder system for 3D volumetric medical data is proposed. The system allows fast access to any 2D image by decoding only the relevant information from each subband image and thus provides minimum decoding time. This will be of immense use for t ...

2006

Wavelets on non-Euclidean manifolds

Iva Bogdanova Vandergheynst

This dissertation investigates wavelets as a multiscale tool on non-Euclidean manifolds. The growing importance of using non-Euclidean manifolds as a geometric model for data comes from the diversity of the data collected. In this work we mostly deal with ...

EPFL2006

Which Wavelet Bases Are the Best for Image Denoising?

Michaël Unser, Thierry Blu, Florian Luisier

We use a comprehensive set of non-redundant orthogonal wavelet transforms and apply a denoising method called SUREshrink in each individual wavelet subband to denoise images corrupted by additive Gaussian white noise. We show that, for various images and a ...

SPIE2005

The Contourlet Transform: An Efficient Directional Multiresolution Image Representation

Martin Vetterli, Minh Do

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can c ...

2005

Generalized Daubechies Wavelets

Michaël Unser, Thierry Blu, Cédric René Jean Vonesch

We present a generalization of the Daubechies wavelet family. The context is that of a non-stationary multiresolution analysis—i.e., a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. ...

IEEE2005

Wavelets on the 2-Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We build wavelets on the 2-Hyperboloid. First, we define dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to

SO_0(1,2)

, we define a family of hyperbolic wavelets. The continuous wavelet transform (CW ...

2004

Wavelet Footprints: Theory, Algorithms and Applications

Martin Vetterli, Pier Luigi Dragotti

In recent years, wavelet-based algorithms have been successful in different signal processing tasks. The wavelet trans- form is a powerful tool because it manages to represent both tran- sient and stationary behaviors of a signal with few transform coeffi- ...

2003

Continuous Wavelet Transform on the Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid

H_+^2

. First, we define a class of suitable dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO ...

2007

Wavelets on the 2-Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We build wavelets on the 2-Hyperboloid. First, we define dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to

SO_0(1,2)

, we define a family of hyperbolic wavelets. The continuous wavelet transform (CW ...

2004