Abstract
A new simple and efficient dual tree analytic wavelet transform based on Discrete Cosine Harmonic Wavelet Transform DCHWT (ADCHWT) has been proposed and is applied for signal and image denoising. The analytic DCHWT has been realized by applying DCHWT to the original signal and its Hilbert transform. The shift invariance and the envelope extraction properties of the ADCHWT have been found to be very effective in denoising speech and image signals, compared to that of DCHWT.
Highlights
The wavelet transform (WT) provides signal compression, denoising and many more desirable processing features
A new simple and efficient dual tree analytic wavelet transform based on Discrete Cosine Harmonic Wavelet Transform Discrete cosine transform (DCT) based harmonic wavelet transform (DCHWT) (ADCHWT) has been proposed and is applied for signal and image denoising
The WT is shift variant, i.e., around singularities, even for a small shift in input signal, there will be a large variation in the energy distribution among WT coefficients at different scales resulting in different WT patterns which have to be considered for further processing [1]
Summary
The wavelet transform (WT) provides signal compression, denoising and many more desirable processing features. The directionality problem remains unsolved as undecimated WT cannot distinguish the two opposing diagonals as it uses separable filters This blindness to such a directionality makes the processing and modeling of image features like ridges and edges difficult. For speech and image signals, the compression provided an adaptive wavelet packet algorithm based on DCHWT has been found to be better than that by DCHWT and that by adaptive Daubechies-2 wavelet packet Further it has been used for efficient and accurate signal decomposition to overcome the cross-terms in Wigner-Ville time frequency distribution the DCTHWT has been extended to realize its shift invariant version. A new dual tree analytic wavelet transform based on DCHWT (ADCHWT) has been proposed and is applied for signal and image denoising. The discrete cosine harmonic wavelet transform and the development of the new dual tree analytic discrete cosine harmonic wavelet transform (ADCHWT) will be considered
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