The curvelet representation of wave propagators is optimally sparse
The curvelet representation of wave propagators is optimally sparse
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DOI：
10.1002/cpa.20078
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发表时间：
2004-07
影响因子：
3
通讯作者：
E. Candès;L. Demanet
中科院分区：
文献类型：
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作者：
E. Candès;L. Demanet
本文认为，曲波提供了一个强大的工具，表示非常一般的线性对称系统的双曲型微分方程。Curvelets是最近开发的多尺度系统[7，9]，其中的元素在细尺度上是高度各向异性的，有效支撑根据抛物线缩放原理在细尺度上形成。我们证明了，对于广泛的一类线性双曲型微分方程，曲波表示的解决方案运营商是最佳稀疏和良好的组织。它是稀疏的，因为矩阵项几乎以指数速度衰减（即，比任何负多项式都快），并且组织得很好，因为极少数不可忽略的条目出现在几个移动的对角线附近。
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.