Scattering in Flatland: Efficient Representations via Wave Atoms

This paper presents a numerical compression strategy for the boundary integral equation of acoustic scattering in two dimensions. These equations have oscillatory kernels that we represent in a basis of wave atoms, and compress by thresholding the small coefficients to zero. -1 -0.5 0 0.5 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 200 400 600 800 1000 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 50 100 150 200 250 300 350 400 Left: a kite-shaped scatterer. Middle: a depiction of the kernel of the double-layer potential for this scatterer, sampled as a 1024x1024 matrix. Right: a zoomed-in view of the sparsity pattern of the "nonstandard wave atom matrix", representing this kernel accurately using only 60,000 matrix elements. This phenomenon was perhaps first observed in 1993 by Bradie, Coifman, and Grossman, in the context of local Fourier bases [5]. Their results have since then been extended in various ways. The purpose of this paper is to bridge a theoretical...

• Type: Journal
• Year: 2010
• Where: FOCM
• Authors: Laurent Demanet, Lexing Ying
• Keywords: FOCM 2010, Multimedia, Nonstandard Wave Atom, Wave Atom, Wave Atom Matrix