Orthonormal Wavelet Basis2.22002/12/042003/02/11IvanSelesnickselesi@taco.poly.eduCharletReedstromcharlet@rice.eduIvanSelesnickselesi@taco.poly.eduorthogonal wavelet basis
An orthonormal wavelet basis is an orthonormal basis of the form
B2j2ψ2jtkjk
The function
ψt is called the wavelet.
The problem is how to find a function
ψt so that the set B is an
orthonormal set.
Haar Wavelet
The Haar basis
(described by Haar in 1910) is an orthonormal
basis with wavelet
ψtψt10t12-112t10
For the Haar wavelet, it is easy to verify that the set
B is an orthonormal set ().
Notation:
ψj,kt2j2ψ2jtk
where j is an index of
scale and k
is an index of location.
If B is an orthonormal set then
we have the wavelet series.
Wavelet seriesxtjkdjkψj,ktdjktxtψj,kt