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Summary: IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 50, NO. 3, MARCH 2002 487
Lifting Scheme for Biorthogonal Multiwavelets
Originated from Hermite Splines
Amir Z. Averbuch and Valery A. Zheludev
Abstract--We present new multiwavelet transforms of multi-
plicity 2 for manipulation of discrete-time signals. The transforms
are implemented in two phases: 1) Pre (post)-processing, which
transforms the scalar signal into a vector signal (and back) and
2) wavelet transforms of the vector signal. Both phases are per-
formed in a lifting manner. We use the cubic interpolatory Her-
mite splines as a predicting aggregate in the vector wavelet trans-
form. We present new pre(post)-processing algorithms that do not
degrade the approximation accuracy of the vector wavelet trans-
forms. We describe two types of vector wavelet transforms that are
dual to each other but have similar properties and three pre(post)-
processing algorithms. As a result, we get fast biorthogonal algo-
rithms to transform discrete-time signals that are exact on sampled
cubic polynomials. The bases for the transform are symmetric and
have short support.
Index Terms--Hermite spline, lifting scheme, multifilter, multi-
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