Image separation using monogenic signal of stationary wavelet transform
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Abstract:
The monogenic signal is a multidimensional generalization of the analytic signal. The monogenic signal of the continuous wavelet transform is called the monogenic wavelet transform. Stationary wavelet transform is a redundant discrete wavelet transform, which is translation-invariant. A new method for blind image source separation based on position-scale information using the monogenic wavelet transform discretized by the stationary wavelet transform is presented.Keywords:
Harmonic wavelet transform
Stationary wavelet transform
Second-generation wavelet transform
Lifting Scheme
Continuous wavelet transform
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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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 scheme for designing virtual instrument of wavelet transform is described. Mathematic model of wavelet analysis function and typical controls is founded and the algorithm is selected and designed. Based on virtual instrument technology, the virtual instrument of wavelet transform is successfully developed. The instrument consists of continuous wavelet transform, discrete wavelet transform, wavelet package decomposition etc, which provide the engineering signal analysis a new manner. The fact is proved, the instrument has extensive using value.
Second-generation wavelet transform
Lifting Scheme
Stationary wavelet transform
Harmonic wavelet transform
Virtual instrumentation
Fast wavelet transform
Continuous wavelet transform
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The wavelet transform is implemented using an optical multichannel correlator with a bank of wavelet transform filters. This approach provides a shift-invariant wavelet transform with continuous translation and discrete dilation parameters. The wavelet transform filters can be in many cases simply optical transmittance masks. Experimental results show detection of the frequency transition of the input signal by the optical wavelet transform.
Second-generation wavelet transform
Harmonic wavelet transform
Stationary wavelet transform
Lifting Scheme
Fast wavelet transform
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Lifting Scheme
Second-generation wavelet transform
Stationary wavelet transform
Harmonic wavelet transform
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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
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Wavelet transform has the characteristic of good space-frequency local area,which makes it become a strong tool in image compression.The wavelet transform based on lifting scheme is called the second-generation wavelet transform.Wavelet lifting scheme provides a new faster realization method for all the first-generation wavelet transform,so that it no more depends on Fourier transform structure.The process of first-generation wavelet transform is divided into three phases of split,prediction and update by lifting scheme.The wavelet transform based on lifting scheme is the static image compression standard of new generation——one of the key algorithms in JPEG 2000.The paper analyses it's application in the basic of researching the lifting scheme.In the end of the paper,the lifting scheme is compared with Mallat algorithm,and the experimental result indicates that the lifting scheme is as double speed as the Mallat algorithm.
Lifting Scheme
Second-generation wavelet transform
Stationary wavelet transform
Harmonic wavelet transform
S transform
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This paper discusses the principle and procedures of the second-generation wavelet trans- form and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method using linear and nonlinear spatial prediction and operators to implement the wavelet transform and to make it reversible. The lifting scheme transform includes three steps: split, predict, and update. Deslauriers-Dubuc (4, 2) wavelet transforms are used to process both synthetic and real data in our second-generation wavelet transform. The processing results show that random noise is effectively suppressed and the signal to noise ratio improves remarkably. The lifting wavelet transform is an efficient algorithm.
Lifting Scheme
Second-generation wavelet transform
Stationary wavelet transform
Harmonic wavelet transform
S transform
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We present a new form of wavelet transform. Unlike the continuous wavelet transform (CWT) or discrete wavelet transform (DWT), the mother wavelet is chosen to be a discrete-time signal and wavelet coefficients are computed by correlating a given discrete-time signal with continuous dilations of the mother wavelet. The results developed are based on the definition of a discrete-time scaling (dilation) operator through a mapping between the discrete and continuous frequencies. The forward and inverse wavelet transforms are formulated. The admissibility condition is derived, and examples of discrete-time wavelet construction are provided. The new form of wavelet transform is naturally suited for discrete-time signals and provides analysis and synthesis of such signals over a continuous range of scaling factors.
Second-generation wavelet transform
Stationary wavelet transform
Harmonic wavelet transform
Lifting Scheme
Cascade algorithm
Continuous wavelet transform
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Lifting Scheme
Second-generation wavelet transform
Stationary wavelet transform
Harmonic wavelet transform
S transform
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Citations (66)