NEW: L. Demanet, L. Ying, Scattering in Flatland: Efficient Representations via Wave Atoms, submitted, 2008. This work is concerned with the boundary integral equations of acoustic scattering, and how to compress their kernel using a nonstandard wave atom matrix.
L. Demanet, L. Ying, Curvelets and Wave Atoms for Mirror-Extended Images, in Proc. SPIE Wavelets XII conf, San Diego, August 2007. This paper shows how the ideas of "wavelets on an interval" can be transposed to wave atoms (and curvelets).
L. Demanet, L. Ying, Wave Atoms and Time Upscaling of Wave Equations, submitted, 2007. This paper shows how wave atoms can be used to numerically compute and compress the Green's function of wave equations in smooth media.
L. Demanet, L. Ying, Wave Atoms and Sparsity of Oscillatory Patterns, to appear in Appl. Comput. Harmon. Anal. (2007). This paper defines wave atoms, details their implementation, and describes an application to sparse representation of oscillatory textures.
L. Villemoes, Wavelet packets with uniform time-frequency localization, Comptes Rendus Math. 335-10 (2002) 793-796. This paper presents the continuous 1D architecture underlying wave atoms.
We would like to thank Emmanuel Candes for support, discussions, and encouragements.