X-lets are directional or geometric extensions of the two-dimensional wavelet concept.
They allow an almost optimal non-adaptive sparse representation of objects with edges.
Some of these transforms require non-separable operations; some of them are highly redundant.
The others are separable or critically sampled.
The X-lets comprises steerable wavelets, curvelets, contourlets, shearlets, wedgelets, beamlets, bandlets, wave atoms, and many others.