In image compression, the wavelet transformation is a state-of-the-art component. Recently, wavelet packet decomposition has received quite an interest. A popular approach for wavelet packet decomposition is the near-...
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In image compression, the wavelet transformation is a state-of-the-art component. Recently, wavelet packet decomposition has received quite an interest. A popular approach for wavelet packet decomposition is the near-best-basisalgorithm using nonadditive cost functions. In contrast to additive cost functions, the wavelet packet decomposition of the near-best-basisalgorithm is only suboptimal. We apply methods from the field of evolutionary computation (EC) to test the quality of the near-best-basis results. We observe a phenomenon: the results of the near-best-basisalgorithm are inferior in terms of cost-function optimization but are superior in terms of rate/distortion performance compared to EC methods.
Smooth local trigonometric bases along with wavelet packet bases have provided a natural setup for the best basis algorithm of Coifiman and Wickerhauser. We consider a best basis algorithm for local trigonometric base...
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Smooth local trigonometric bases along with wavelet packet bases have provided a natural setup for the best basis algorithm of Coifiman and Wickerhauser. We consider a best basis algorithm for local trigonometric bases with a cost function that only depends on the local behavior of the signal near the points where the local trigonometric functions overlap. The benefit is that the complexity of the algorithm is much lower than using a standard cost function in the best basis algorithm. We compare the performance of the algorithm to the best basis algorithm using an l(1)-norm as cost function on several test signals. (C) 2002 Elsevier Science B.V. All rights reserved.
Adapted wavelet analysis in the sense of wavelet packet algorithms is a highly relevant procedure in different types of applications, like, e.g. data compression, feature extraction, classification problems, data anal...
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Adapted wavelet analysis in the sense of wavelet packet algorithms is a highly relevant procedure in different types of applications, like, e.g. data compression, feature extraction, classification problems, data analysis, numerical mathematics, etc. Given a large or high-dimensional data set the computational demand is too high for interactive or "nearly-interactive" processing. Therefore, parallel processing is one of the possibilities to accelerate the processing speed. In this case, special attention has to be paid towards handling of the large amount of data in addition to the proper organization of the computations. We investigate different data decomposition approaches, border handling techniques and programming paradigms. The memory consuming decomposition into a given arbitrary basis after adaptive basis choice is resolved by a localized decomposition strategy. (C) 2001 Elsevier Science B.V. All rights reserved.
We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their "dual" domains by incorporating the "natural" distances between graph Laplacian eigenvectors, rather...
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We introduce a set of novel multiscale basis transforms for signals on graphs that utilize their "dual" domains by incorporating the "natural" distances between graph Laplacian eigenvectors, rather than simply using the eigenvalue ordering. These basis dictionaries can be seen as generalizations of the classical Shannon wavelet packet dictionary to arbitrary graphs, and do not rely on the frequency interpretation of Laplacian eigenvalues. We describe the algorithms (involving either vector rotations or orthogonalizations) to construct these basis dictionaries, use them to efficiently approximate graph signals through the bestbasis search, and demonstrate the strengths of these basis dictionaries for graph signals measured on sunflower graphs and street networks.
All experiments of pressure fluctuations were carried out in a bubble column with a moderately large column of 0.376 in ID. The recently developed technique of wavelet packet transform based on localized wavelet funct...
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All experiments of pressure fluctuations were carried out in a bubble column with a moderately large column of 0.376 in ID. The recently developed technique of wavelet packet transform based on localized wavelet functions is applicable to analysis of the fluctuating signals. The time series of pressure fluctuation signals have been analyzed by means of wavelet packet transform components, decomposition through best basis algorithm and time-frequency representation. By resorting to this technique, the objects in bubbly flow regime have fine scales and frequencies than ones in chum-turbulent flow regime. Thus, this wavelet packet transform method enables us to obtain the frequency content of local complex flow behaviors in a bubble column.
We present a heuristic solution for B-term approximation of 1-D discrete signals using Tree-Structured Haar (TSH) transforms. Our solution consists of two main stages: bestbasis selection and greedy approximation. In...
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ISBN:
(纸本)9780819474957
We present a heuristic solution for B-term approximation of 1-D discrete signals using Tree-Structured Haar (TSH) transforms. Our solution consists of two main stages: bestbasis selection and greedy approximation. In addition, when approximating the same signal with different B constraints or error metrics, our solution also provides the flexibility of reducing overall computation time of approximation by increasing overall storage space. We adopt a lattice structure to index basis vectors, so that one index value can fully specify a basis vector. Based on the concept of fast computation of TSH transform by butterfly network, we also develop an algorithm for directly deriving butterfly parameters and incorporate it into our solution. Results show that, when the error metric is either normalized l(1)-norm or normalized l(2)-norm, our solution has comparable (sometimes better) approximation quality with prior data synopsis algorithms.
For seismic resistant design of critical structures, a dynamic analysis, either response spectrum or time history is frequently required. Owing to the lack of recorded data and the randomness of earthquake ground moti...
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For seismic resistant design of critical structures, a dynamic analysis, either response spectrum or time history is frequently required. Owing to the lack of recorded data and the randomness of earthquake ground motion that may be experienced by structure in the future, usually it is difficult to obtain recorded data which fit the requirements (site type, epicenteral distance, etc.) well. Therefore, the artificial seismic records are widely used in seismic designs, verification of seismic capacity and seismic assessment of structures. The purpose of this paper is to develop a numerical method using Artificial Neural Network (ANN) and wavelet packet transform in bestbasis method which is presented for the decomposition of artificial earthquake records consistent with any arbitrarily specified target response spectra requirements. The ground motion has been modeled as a non-stationary process using wavelet packet. This study shows that the procedure using ANN-based models and wavelet packets in best-basis method are applicable to generate artificial earthquakes compatible with any response spectra. Several numerical examples are given to verify the developed model.
Event-related potentials (ERPs) are brain electrical potentials associated with sensory and cognitive processing. ERP researchers typically wish to separate a recorded time series into functionally distinct component ...
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Event-related potentials (ERPs) are brain electrical potentials associated with sensory and cognitive processing. ERP researchers typically wish to separate a recorded time series into functionally distinct component waveforms, and to estimate the effects of experimental conditions on each component. We present an integrated statistical approach to the decomposition of single-channel ERPs and to inference concerning the component waveforms and the effects of experimental conditions on the amplitude and latency (lag from stimulus presentation) of each component. A wavelet packet model of a single individual's data defines a unique decomposition based on prior time/frequency information and variation among experimental conditions. A particular orthogonal wavelet packet basis is selected using the best basis algorithm with a special cost function that incorporates prior information. Our statistical model allows individual-specific parameters to vary randomly among individuals. Because the number of observations on each individual is several orders of magnitude greater than the number of independent individuals, we fit our mixed model using a two-stage approach. In the first stage, a separate wavelet packet model is fit to each individual's data;in the second stage, the parameter estimates from the first stage are analyzed. We evaluated our method using numerical experiments based on design and analysis concepts that are common in applied statistics, but that are rarely used in evaluation of new statistical methods. We applied our methods to auditory evoked responses of cats recorded before and after lesions of the brain association cortex and at several stimulus rates. Our data analysis revealed a surprising lesion effect on the auditory brainstem response.
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