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The curvelet representation of wave propagators is optimally sparse

E. Candès,L. Demanet

Published 2004 in Communications on Pure and Applied Mathematics

ABSTRACT

This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system [7, 9] in which the elements are highly anisotropic at fine scales, with effective support shaped according to the parabolic scaling principle width ≈ length2 at fine scales. We prove that for a wide class of linear hyperbolic differential equations, the curvelet representation of the solution operator is both optimally sparse and well organized. It is sparse in the sense that the matrix entries decay nearly exponentially fast (i.e., faster than any negative polynomial) and well organized in the sense that the very few nonnegligible entries occur near a few shifted diagonals.

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