Critically sampled composite wavelets

Wavelets with composite dilations were introduced to provide a framework for the construction of waveforms defined not only at various scales and locations but also at various orientations. The shearlet system, which provides optimally sparse representations of images with edges, is a particular well-known example of these systems. In this work, we develop critically sampled wavelet transforms with composite dilations for the purpose of image coding. We show that these new critically sampled transforms can achieve much better non-linear approximation rates for images containing edges than traditional discrete wavelet transforms or even more sophisticated multiscale transforms such as the critically sampled contourlet transform.