Image denoising research based on lifting wavelet transform and threshold optimization
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In many application occasions, symmetry or antisymmetry of wavelet is fairly important to signal processing. In mid 1990s, Sweldens advanced the lifting wavelet transform. Compared with the first-generation wavelet, the lifting scheme could complete the wavelet transform currently without allocating additional memory, so it is easy to achieve with chips; the algorithm is simple and suitable for parallel processing, which makes the computation more fast; it could realize integral wavelet transform, which has wide potential applications. The paper analyzes the wavelet lifting algorithm and its poly-phase decomposition mechanism and approaches the image processing algorithm based on lifting wavelet transform. Since the structure of lifting wavelet is independent of Fourier transform, conducting image fusion by using the lifting wavelet could improve the processing speed and save memory.Keywords:
Second-generation wavelet transform
Lifting Scheme
Stationary wavelet transform
Harmonic wavelet transform
Second-generation wavelet transform
Stationary wavelet transform
Harmonic wavelet transform
Lifting Scheme
Cascade algorithm
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Although Optical wavelet transform has some advantages over discrete wavelet transform, but the mother wavelets to used are very few. That limits the signal processing ability of optical wavelet transform. Without scaling functions, the multiresolution analysis of a mother wavelet is not complete. In this paper, almost all the mother wavelets used in discrete wavelet transform are introduced into optical wavelet transform. Based on the analysis, we find whether the mother wavelets have analytical forms is not a necessary condition for implementing them in optical wavelet transform. Optical wavelet transform only needs to obtain the 2D approximations of wavelet functions. Then, with the cascade algorithm, the 1D approximations of scaling and wavelet functions are computed. By the scheme of 2D separable wavelet transform, the approximations of 2D scaling and wavelet functions are constructed. So mother wavelets frequently utilized in discrete wavelet transform are introduced into optical wavelet transform. With the increase of mother wavelet for selection, it is natural to classify optical wavelet transform into separable and non-separable cases as it does in discrete wavelet transform. Since the mothers introduced by the method in this paper are separable, they are included in the separable optical wavelet transform. And the advantages of the separable mothers are listed with corresponding examples.
Stationary wavelet transform
Second-generation wavelet transform
Lifting Scheme
Harmonic wavelet transform
Cascade algorithm
Fast wavelet transform
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Wavelet transform has been widely applied to time-frequency signal analysis, image processing (enhancement, feature extraction, etc.), and target detection. Since wavelet transform is a convolution process between an input and a large number of wavelet bases, the computation load increases nonlinearly with the sizes of the input and the wavelet. Near real-time optical wavelet transform [1-3] could be accomplished by using an optical correlator architecture. The processing speed of optical wavelet transform is independent of the size of the wavelet filter and is only limited to the updating speed of the spatial light modulator.
Second-generation wavelet transform
Stationary wavelet transform
Lifting Scheme
Harmonic wavelet transform
Fast wavelet transform
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Recently, the second generation wavelet which is lifting scheme of the first generation wavelet has attached much attention, because it keeps the good characteristics of the first generation wavelet transform and gets over the limitation of the first generate wavelet transform. This paper expounds of the lifting scheme and the excellent characteristics of the second generation wavelet transform, and makes comparison between the first generation wavelet ransform(DWT) and the second generation wavelet transform(LWT).
Lifting Scheme
Second-generation wavelet transform
Stationary wavelet transform
Harmonic wavelet transform
Cascade algorithm
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The dual-tree complex wavelet transform is considered a relatively recent improvement for the discrete wavelet transform. In this paper, the applicability of such transform in the problem of speech enhancement is evaluated. For this purpose, a nonthreshold scheme is proposed. Two filters, one for the imaginary part and other for the real part of complex wavelet coefficients were designed. These two real filters were then averaged to obtain the final filter. A uniform noise reduction was performed for all wavelet scales. Simulation results show that, together, nonthresholding scheme and dual-tree complex wavelet transform obtained consistently results.
Second-generation wavelet transform
Complex wavelet transform
Stationary wavelet transform
Harmonic wavelet transform
Lifting Scheme
Tree (set theory)
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The results of the wavelet analysis application to the ultrawideband (UWB) signal investigation are introduced. The continuous wavelet transform, the analytic wavelet transform, the discrete wavelet transform, the wavelet packets, the stationary wavelet transform and the Kravchenko-Rvachev analytic wavelets based on the atomic functions have been used to the analysis of the UWB signals and processes.
Second-generation wavelet transform
Harmonic wavelet transform
Stationary wavelet transform
Lifting Scheme
Fast wavelet transform
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A new extended adaptive wavelet transform method based on the Claypoole adaptive wavelet transform was proposed.The degrees of Sweldens interpolating polynomial from the odd to the positive integer were extended by the method to extend the choice of the vanishing moments of the wavelet.The extended adaptive wavelet and the adaptive wavelet were used for filtering the signal.The simulated results show that the extended adaptive wavelet transform can get ideal application effect and supply more wavelets.
Stationary wavelet transform
Second-generation wavelet transform
Lifting Scheme
Harmonic wavelet transform
Cascade algorithm
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In many application occasions, symmetry or antisymmetry of wavelet is fairly important to signal processing. In mid 1990s, Sweldens advanced the lifting wavelet transform. Compared with the first-generation wavelet, the lifting scheme could complete the wavelet transform currently without allocating additional memory, so it is easy to achieve with chips; the algorithm is simple and suitable for parallel processing, which makes the computation more fast; it could realize integral wavelet transform, which has wide potential applications. The paper analyzes the wavelet lifting algorithm and its poly-phase decomposition mechanism and approaches the image processing algorithm based on lifting wavelet transform. Since the structure of lifting wavelet is independent of Fourier transform, conducting image fusion by using the lifting wavelet could improve the processing speed and save memory.
Second-generation wavelet transform
Lifting Scheme
Stationary wavelet transform
Harmonic wavelet transform
Cite
Citations (5)
Wavelet expansions have received a lot of interest in the EMC literature. In fact they have been widely used in electromagnetics to expand electrical quantities either in time or space domain, allowing an adaptive representation of the solution. It has been shown that the discrete wavelet transform is just a particular case of the discrete wavelet packet transform. The paper deals with the comparison of the standard wavelet transform versus the wavelet packet transform in studying MTLs, pointing out the advantages in using the latter approach respect to the former one. In particular an appropriate choice of the wavelet packet basis is shown to be effective in reducing the computation time and memory storage requirements. Several validations and numerical examples are presented.
Second-generation wavelet transform
Stationary wavelet transform
Lifting Scheme
Harmonic wavelet transform
Cascade algorithm
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Citations (2)
Noise has been a major limitation to partial discharge (PD) measurement. It is crucial to suppress noise prior to any PD data analysis. Recent research shows that the discrete wavelet transform, wavelet packet transform and stationary wavelet transform techniques have all achieved good effect in noise rejection in PD measurement. This paper compares the effectiveness and computing time required of the three types of wavelet transform methods when applied to simulated PD data in presence of white noise and sinusoidal interference
Stationary wavelet transform
Second-generation wavelet transform
Harmonic wavelet transform
Lifting Scheme
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Citations (43)