Bandelets are an
orthonormal basis
In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite Dimension (linear algebra), dimension is a Basis (linear algebra), basis for V whose vectors are orthonormal, that is, they are all unit vec ...
that is adapted to geometric boundaries. Bandelets can be interpreted as a warped
wavelet
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 n ...
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 n ...
, many of the results follow. Similar approaches to take account of geometric structure were taken for
contourlet In image processing, 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 Laplacia ...
s and
curvelet
Curvelets are a non-Adaptive-additive algorithm, adaptive technique for multi-scale Object (computer science), object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processin ...
s.
See also
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Wavelet
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 n ...
*
Multiresolution analysis
A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms (DWT) and the justification for the algorithm of the fast wavelet transform (FWT). It was int ...
*
Scale space
Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal the ...
References
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External links
Bandelet toolboxon MatLab Central
Wavelets
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