Design and implementation of Wavelet Transform using Adaptive Genetic Algorithms and Analog filters
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This paper presents a low power and low-voltage analog switched-current (SI) filters implementation of wavelet transform (WT) for real-time requirements in signal processing.First, an adaptive genetic algorithm (AGA) is used to calculate the transfer function of the filters, whose impulse response is the required wavelet base.This approach improves the approximation performance than the previous traditional approaches and allows for the circuit implementation of any other wavelet base.Next, the approximation wavelet function is implemented using SI filters based on the cascade structure with SI differentiators as main building blocks.The Gaussian wavelet is selected as an example to illustrate the design procedure.Simulations demonstrate that the proposed method implements WT is an excellent way.Keywords:
Differentiator
Stationary wavelet transform
Second-generation wavelet transform
Cascade algorithm
Recursive wavelet filters and an alternative algorithm for implementing wavelet transform are presented in this paper. The recursive filters use previously calculated (past) wavelet coefficients as inputs to calculate the current wavelet coefficient, and provide the same transform results as convolutional FIR and lifting wavelet filters. The coefficients of the recursive filters are derived from those of conventional FIR wavelet filters. The wavelet transform with recursive filters requires a smaller amount of memory and is easy to implement in hardware. Another important advantage of the recursive filters is that perfect reconstruction can be easily achieved using recursive wavelet filters if a sequence of pixels to be transformed is extended by boundary pixel repetition. Boundary pixel repetition can be more efficient than the widely used method of symmetric extension for image and video coding.
Stationary wavelet transform
Second-generation wavelet transform
Lifting Scheme
Cascade algorithm
Harmonic wavelet transform
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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 packet transform analyzes signals more finely than wavelet transform does. This advantage can be utilized in optical wavelet transform. To introduce wavelet packet transform into optics, mother wavelets that have scaling functions must be used. If the scaling function does not have analytical formula, its approximation can be computed using the cascade algorithm. With the refinement relationship, its wavelet function can by calculated. After the 1-D wavelet packet bases are obtained, 2-D separable wavelet packet bases can be constructed for optical wavelet packet transform. As an example, a volume holographic opto-electronic system is proposed to fulfill joint best basis selection for a face image bank with the mother Db3.
Stationary wavelet transform
Second-generation wavelet transform
Harmonic wavelet transform
Cascade algorithm
Lifting Scheme
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The richness of wavelet transformation is known in many fields. There exist different classes of wavelet filters that can be used depending on the application. In this paper, we propose an IEEE 754 floating-point lifting-based wavelet processor that can perform various forward and inverse Discrete Wavelet Transforms (DWTs) and Discrete Wavelet Packets (DWPs). Our architecture is based on processing elements that can perform either prediction or update on a continuous data stream in every two clock cycles. We also consider the normalization step that takes place at the end of the forward DWT/DWP or at the beginning of the inverse DWT/DWP. To cope with different wavelet filters, we feature a multi-context configuration to select among various DWTs/DWPs. Different memory sizes and multi-level transformations are supported. For the 32-bit implementation, the estimated area of the proposed processor with 2times512 words memory and 8 PEs in a 0.18-mum process is 3.7 mm square and the estimated operating speed is 353 MHz.
Second-generation wavelet transform
Stationary wavelet transform
Lifting Scheme
Cascade algorithm
Normalization
Harmonic 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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An effective algorithm combining optimal wavelet packet basis (OWPB) algorithm and translation-invariant (TI) wavelet transform algorithm was put forward. Based on wavelet packet analysis, according to least cost function principle, OWPB of signal decomposition was obtained, which would better match the requested localization in the frequency domain and ensure an efficient de-noising: Firstly, the estimated OWPB coefficients were gained by using thresholding methods, and then based on inverse discrete wavelet packet transform (IDWPT), the de-noised signals were obtained by using estimated OWPB coefficients. Because wavelet thresholding de-noising methods would result in Pseudo-Gibbs phenomenon in the neighborhood of discontinuities, in order to suppress it, this study adopt TI wavelet transform algorithm. The results of experiment indicated the algorithm proposed in the pager was better than traditional wavelet packet transform (WPT) thresholding de-noising methods.
Second-generation wavelet transform
Stationary wavelet transform
Cascade algorithm
Harmonic wavelet transform
Lifting Scheme
Fast wavelet transform
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Though many DWT-based or wavelet packet watermarking algorithms have been presented,few of them refer to using such novel wavelet concepts as promotion wavelet and combination wavelet. This paper firstly introduces the digital watermarking based on wavelet transform,and then proposes the novel algorithms with promotion wavelet and combination wavelet. At last, it discusses on the research direction and application prospect.
Second-generation wavelet transform
Stationary wavelet transform
Lifting Scheme
Cascade algorithm
Harmonic wavelet transform
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Based on the non-local means( NL-means) filter algorithm,in order to improve the image quality,a NL-means algorithm based on wavelet packet transform is proposed. Firstly,the image is transformed by the wavelet packet,and the wavelet domain coefficients are applied to estimate the Gaussian noise parameters of the image,then the similarity of the high-frequency subband's wavelet coefficients is calculated as the weights to adjust the wavelet coefficients,finally the image is reconstructed by the inverse wavelet packet transform. Experiment results show that this algorithm can preserve the edge detail information effectively,and get a superior denoising performance than the original non-local mean algorithm.
Stationary wavelet transform
Second-generation wavelet transform
Cascade algorithm
Lifting Scheme
Non-Local Means
Fast wavelet transform
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Wavelet packet theory is employed to adaptive multiuser detection, and wavelet packet transform based adaptive multiuser detection algorithm is presented in this paper. This novel adaptive multiuser detection algorithm uses wavelet packet transform as the preprocessing, and wavelet packet transformed signal uses least mean squares (LMS) algorithm to implement adaptive multiuser detection. This algorithm makes use of wavelet packet transform to divide the wavelet space, which shows that wavelet packet transform has a better decorrelation ability and leads to better convergence. White noise can be wiped off under wavelet packet transform, according to different characteristics of signal and white noise under the wavelet packet transform. Theoretical analysis and simulations demonstrate that this algorithm converges faster than the conventional adaptive multiuser detection algorithm and wavelet transform based multiuser detection algorithm, and it also has the better performance. Simulation results also reveal that the algorithm convergence relates closely to wavelet base and decomposition series, and show that the algorithm convergence gets better as with the increasing of decomposition series, and for the same series of wavelet base the algorithm convergence gets better as with the increasing of wavelet base regularity. Finally the algorithm is no more complex, and can be implemented easily.
Stationary wavelet transform
Second-generation wavelet transform
Cascade algorithm
Lifting Scheme
Harmonic wavelet transform
Fast wavelet transform
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Second-generation wavelet transform
Stationary wavelet transform
Lifting Scheme
Cascade algorithm
Harmonic wavelet transform
Cite
Citations (4)