Design of signal dependent wavelet transform

Many wavelet design techniques build adaptive wavelets from existing wavelets. However, most of the techniques do not design wavelet directly of the signal of interest. Conventional signal dependent transforms are Karhunen-Loeve transform and Singular Value Decomposition whose basis function depends on statistics of an input signal. Signal-dependent transform is considered to be best among all linear transformations with respect to energy compaction. Likewise, wavelets are best known for image compression, many researchers are interested in using wavelets for detection or recognition. Choosing appropriate wavelet for a given application is a challenging task. Therefore, there is a need of designing wavelet to match a signal shape which increases performance for detection or identification applications. J. Chapa and R. Rao [15] have introduced algorithms for designing wavelet to match the signal shape. The construction of direct wavelet function which will look like the signal and whose family of 2
^-p/2
ψ(2
^-p
t - q) wavelets generate an orthonormal Riesz basis of L
²
(R) are established. In this method, numerical algorithms are used for finding matched wavelet amplitude spectra and group delays using sampled data which are signal dependent wavelets. Orthonormal scaling function (father wavelet function) is obtained by applying orthonormal multiresolution analysis (OMRA) conditions on input signal.