Bandelets are an
orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space ''V'' with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, ...
that is adapted to geometric boundaries. Bandelets can be interpreted as a warped
wavelet 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
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the num ...
, many of the results follow. Similar approaches to take account of geometric structure were taken for
contourlet
Contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries. The contourlet transform has a fast implementation based on a Laplacian pyramid decompositi ...
s and
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.
Wavelets generalize the Fou ...
s.
See also
*
Wavelet
*
Multiresolution analysis
*
Scale space
References
*
*
External links
Bandelet toolboxon MatLab Central
Wavelets
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