Wave atoms are a recent addition to the repertoire of mathematical transforms of computational harmonic analysis. They come either as an orthonormal basis or a tight frame of directional wave packets, and are particularly well suited for representing oscillatory patterns in images. They also provide a sparse representation of wave equations, hence the name wave atoms.
support size ~ sqrt(wavelength)
while retaining an isotropic aspect ratio. As a result, wave atoms precisely interpolate between Gabor (fixed support size) and wavelets (support size ~ wavelength).
Wave atoms have a sharp frequency localization that cannot be obtained from filterbank-based wavelet packets. In 2002, Lars Villemoes presented an elegant alternative 1D wave packet design with proper time-frequency localization, that we have built upon and expanded into what has become the Matlab WaveAtom toolbox. The software now includes several variants of the transform: 1D, 2D, and 3D; orthobasis and two different tight frames including shift-invariant; periodized and mirror-extended at image edges. A C++ version is also available.