Diffusion Wavelets

Diffusion Wavelets (2004)

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by Ronald R. Coifman , Mauro Maggioni

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Datum	Value	Source
TITLE	Diffusion Wavelets	user correction
AUTHOR NAME	Ronald R. Coifman	user correction
AUTHOR AFFIL	Program in Applied Mathematics; Department of Mathematics; Yale University; New Haven,CT,06510; U.S.A.	user correction
AUTHOR NAME	Mauro Maggioni	user correction
AUTHOR AFFIL	Program in Applied Mathematics; Department of Mathematics; Yale University; New Haven,CT,06510; U.S.A.	user correction
ABSTRACT	We present a multiresolution construction for efficiently computing, compressing and applying large powers of operators that have high powers with low numerical rank. This allows the fast computation of functions of the operator, notably the associated Green’s function, in compressed form, and their fast application. Classes of operators satisfying these conditions include diffusion-like operators, in any dimension, on manifolds, graphs, and in non-homogeneous media. In this case our construction can be viewed as a far-reaching generalization of Fast Multipole Methods, achieved through a different point of view, and of the non-standard wavelet representation of Calderón-Zygmund and pseudodifferential operators, achieved through a different multiresolution analysis adapted to the operator. We show how the dyadic powers of an operator can be used to induce a multiresolution analysis, as in classical Littlewood-Paley and wavelet theory, and we show how to construct, with fast and stable algorithms, scaling function and wavelet bases associated to this multiresolution analysis, and the corresponding downsampling operators, and use them to compress the corresponding powers of the operator. This allows to extend multiscale signal processing to general spaces (such as manifolds and graphs) in a very natural way, with corresponding fast algorithms.	SVM HeaderParse 0.2
YEAR	2004	user correction
CITATIONS	76 found	ParsCit 1.0