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Wavelet transform on manifolds: old and new approaches

Publications associées (81)

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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

Stereographic Wavelet Frames on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this paper we exploit the Continuous Wavelet Transform (CWT) on the two dimensional sphere, introduced previously by two of us, to build associated Discrete Wavelet Frames. We first explore half-continuous frames, i.e., frames where the position remains ...

2005

Correspondence principle between spherical and Euclidean wavelets

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the ...

2005

Stereographic Frames of Wavelets on the Sphere

Pierre Vandergheynst, Laurent Jacques, Iva Bogdanova Vandergheynst

In this technical report the Discrete Wavelet Frames are build on the already existing Spherical Continuous Wavelet Transform. The spherical half-continuous frames are explored, i.e when the position on the sphere is kept continuous variable. Then, the con ...

2004

Replacement manifolds: A method to uniformize semiclassical wave functions

Jiri Vanicek

We present a semiclassical technique that relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold structure gives poor o ...

2001

Solving the p-Laplacian on manifolds

Marc Troyanov

We prove in this paper that the equation

Delta _{p}u+h=0

on a p-hyperbolic manifold M has a solution with p-integrable gradient for any bounded measurable function h : M -> R with compact support. ...

2000

Solving the $p$-Laplacian on manifolds

Marc Troyanov

We prove in this paper that the equation

\Delta _{p}u+h=0

on a

p

- hyperbolic manifold

M

has a solution with

p

-integrable gradient for any bounded measurable function

h : M \to \mathbb R

with compact support. ...

2000

The aquaporin sidedness revisited

Henning Paul-Julius Stahlberg, Andreas Engel

Aquaporins are transmembrane water channel proteins, which play important functions in the osmoregulation and water balance of microorganisms, plants, and animal tissues. All aquaporins studied to date are thought to be tetrameric assemblies of four subuni ...

Elsevier BV2000

Wavelets on the 2-sphere and related manifolds

Pierre Vandergheynst

We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3) × R*+, ...

1999

A route pre-computation algorithm for integrated services networks

Jean-Yves Le Boudec

We provide an algorithm for computing best paths on a graph where edges have a multidimensional cost, one dimension representing delay, the others representing available capacity. Best paths are those which guarantee maximum capacity with least possible de ...

1995