Bandelets are an orthonormal basis

Basis

Basis may refer to* Cost basis, in income tax law, the original cost of property adjusted for factors such as depreciation.* Basis of futures, the value differential between a future and the spot price...

 that is adapted to geometric boundaries. Bandelets can be interpreted as a warped wavelet

Wavelet

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have...

 basis. The motivation behind bandelets is to perform a transform on functions defined as smooth functions on smoothly bounded domains. As bandelet construction utilizes wavelets, many of the results follow. Similar approaches to take account of geometric structure were taken for contourlet

Contourlet

Contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries...

s and curvelet

Curvelet

Curvelets are a non-adaptive technique for multi-scale object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processing and scientific computing....

s.

External links

• Bandelet toolbox on MatLab Central
• Surface Compression With Geometric Bandelets. Gabriel Peyré and Stéphane Mallat, ACM Transactions on Graphics, Vol. 24(3), (Proc. of SIGGRAPH'05), p. 601-608, Jul. 2005. PDF doi:10.1145/1073204.1073236