Showing papers on "Biorthogonal system published in 2001"

Multiresolution time-domain algorithm using CDF biorthogonal wavelets

Abstract: A new approach to the multiresolution time-domain (MRTD) algorithm is presented in this paper by introducing a field expansion in terms of biorthogonal scaling and wavelet functions. Particular focus is placed on the Cohen-Daubechies-Feauveau (CDF) biorthogonal-wavelet class, although the methodology is appropriate for general biorthogonal wavelets. The computational efficiency and numerical dispersion of the MRTD algorithm are addressed, considering several CDF biorthogonal wavelets, as well as other wavelet families. The advantages of the biorthogonal MRTD method are presented, with emphasis on numerical issues.

Biorthogonal approach for explicitly correlated calculations using the transcorrelated Hamiltonian

Abstract: A biorthogonal formulation is applied to the non-Hermite transcorrelated Hamiltonian, which treats a large amount of the dynamic correlation effects implicitly. We introduce biorthogonal canonical orbitals diagonalizing the non-Hermitian Fock operator. We also formulate many-body perturbation theory for the transcorrelated Hamiltonian. The biorthogonal self-consistent field followed by the second order perturbation theory are applied to some pilot calculations including small atoms and molecules.

Biorthogonal partners and applications

Abstract: Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications.

Genetic algorithm wavelet design for signal classification

Abstract: Biorthogonal wavelets are applied to parse multiaspect transient scattering data in the context of signal classification. A language-based genetic algorithm is used to design wavelet filters that enhance classification performance. The biorthogonal wavelets are implemented via the lifting procedure and the optimization is carried out using a classification-based cost function. Example results are presented for target classification using measured scattering data.

Commutation for Irregular Subdivision

Abstract: We present a generalization of the commutation formula to irregular subdivision schemes and wavelets. We show how, in the noninterpolating case, the divided differences need to be adapted to the subdivision scheme. As an example we include the construction of an entire family of biorthogonal compactly supported irregular knot B-spline wavelets starting from Lagrangian interpolation.

Application of biorthogonal interpolating wavelets to the Galerkin scheme of time dependent Maxwell's equations

Abstract: A family of biorthogonal interpolating wavelets has been applied to time-domain electromagnetic field modeling through the wavelet-Galerkin scheme. The scaling functions are the Deslauriers-Dubuc interpolating functions and the wavelets are the shifted and contracted version of the scaling functions. This set of bases yields a simple algorithm for the solution of Maxwell's equations in time domain due to their interpolation properties. The derivation of the algorithm is presented in this paper, followed by a series of numerical verifications on some resonant structures.

Raising Multiwavelet Approximation Order Through Lifting

Abstract: Given a pair of biorthogonal, compactly supported multiwavelets, we present an algorithm for raising their approximationorders to any desired level, using one lifting step and one dual lifting step. Free parameters in the algorithm are explicitly identified, and can be used to optimize the result with respect to other criteria.

Generalized lapped biorthogonal transform embedded inverse discrete cosine transform and low bit rate video sequence coding artifact removal

Abstract: A generalized lapped biorthogonal transform embedded inverse discrete cosine transform (ge-IDCT) (20), as an alternative to the inverse discrete cosine transform (IDCT) within a system for still image compression. The ge-IDCT (20) takes advantage of the DCT (18) front end of the generalized lapped biorthogonal transform (GLBT) in inverse transforming the DCT (18) coefficients. Non-linear weighting is used in the embedded lapped transform domain (16), so that the ge-IDCT (20) can reconstruct the signal with alleviated blockishness. In another embodiment, the disclosed system includes a post-processing method to reduce anomalies caused by blocking artifacts by applying a lapped orthogonal transform-embedded inverse discrete cosine transform (le-IDCT), as a substitute for the usual inverse DCT (18). For the reduction of ringing artifacts, a nonlinear robust filter is applied to the decoded picture frame.

Instanton Dominance of Topological Charge Fluctuations in QCD

Abstract: We consider the local chirality of near-zero eigenvectors from Wilson- Dirac and clover improved Wilson-Dirac lattice operators as proposed recently by Horvath et al. We studied finer lattices and repaired for the loss of orthogonality due to the non-normality of the Wilson-Dirac matrix. As a result we do see a clear double peak structure on lattices with resolutions higher than 0.1 fm. We found that the lattice artifacts can be considerably reduced by exploiting the biorthogonal system of left and right eigenvectors. We conclude that the dominance of in- stantons on topological charge fluctuations is not ruled out by local chirality measurements.

Parallel Computation of Wavelet Transforms Using the Lifting Scheme

Abstract: The lifting scheme l14r is a method for construction of biorthogonal wavelets and fast computation of the corresponding wavelet transforms. This paper describes a message–passing parallel implementation in which high efficiency is achieved by a modified data–swapping approach allowing communications to overlap computations. The method illustrated by application to Haar and Daubechies (D4) wavelets. Timing and speed–up results for the Cray T3E and the Fujitsu AP3000 are presented.

Multiresolution Methods for Reduced-Order Models for Dynamical Systems

Abstract: Reduced-orderinput/output models arederived for a class of nonlinearsystems by utilizing wavelet approximationsof kernels appearing in Volterra series representations. Although Volterra series representationsof nonlinear system input/output have been understood from a theoretical standpoint for some time, their practical use has been limited as a result of the dimensionality of approximations of the higher-order, nonlinear terms. In general, wavelets and multiresolution analysis have shown considerable promise for the compression of signals, images, and, most importantly here, some integral operators. Unfortunately, causal Volterra series representations are expressed in terms of integrals that are restricted to products of half-spaces, and there is a signie cant dife culty in deriving wavelets that are appropriate for Volterra kernel representations that are restricted to semi-ine nite domains. In addition, it is necessary to derive Volterra kernel expansions that are consistent with the method of sampling used to obtain the input and output data. This paper derives discrete approximations for truncated Volterra series representations in termsof a specie cclass of biorthogonal wavelets. When a zero-orderhold is used for both the input and output signals, it is shown that a consistent approximation of the input/output system is achieved for a specie c choice of biorthogonal wavelet families. This family is characterized by the fact that all of the wavelets are biorthogonal with respect to the characteristic function of the dyadic intervals used to dee ne the zero-order hold. It is also simple to show that an arbitrary choice of wavelet systems will not, in general, provide a consistent approximation for arbitrary input/output mappings. Numerical studies of the derived methodologies are carried out by using experimental pitch/plunge response data from the TAMU Nonlinear Aeroelastic Testbed.

Application of biorthogonal interpolating wavelets to the Galerkin scheme of time dependent Maxwell's equations

Abstract: A family of biorthogonal interpolating wavelets has been applied to time-domain electromagnetic field modeling through the wavelet-Galerkin scheme. The scaling functions are the Deslauriers-Dubuc interpolating functions and the wavelets are the shifted and contracted version of the scaling functions. This set of bases yields a simple algorithm for the solution of Maxwell's equations in time domain due to their interpolation properties. The derivation of the algorithm is presented in this paper, followed by a series of numerical verification on some resonant structures.

A characterization of wavelet families arising from biorthogonal MRA’s of multiplicity d

Abstract: In this article we give a necessary and sufficient condition for a pair of wavelet families $$\Psi = \{ \psi ^1 ,...,\psi ^L \} , \tilde \Psi = \{ \tilde \psi ^1 ,...,\tilde \psi ^L \} $$ in L2(ℝ n ), to arise from a pair of biorthogonal MRA’s. The condition is given in terms of simple equations involving the functions ψl and $$\tilde \psi ^\ell $$ . To work in greater generality, we allow multiresolution analyses of arbitrary multiplicity, based on lattice translations and matrix dilations. Our result extends the characterization theorem of G. Gripenberg and X. Wang for dyadic orthonormal wavelets in L2(ℝ),and includes, as particular cases, the sufficient conditions of P. Auscher and P.G. Lemarie in the biorthogonal situation.

Greedy algorithms and bestm-term approximation with respect to biorthogonal systems

Abstract: The article extends upon previous work by Temlyakov, Konyagin, and Wojtaszczyk on comparing the error of certain greedy algorithms with that of best m-term approximation with respect to a general biorthogonal system in a Banach space X. We consider both necessary and sufficient conditions which cover most of the special cases previously considered. Some new results concerning the Haar system in L1, L∞, and BMO are also included.

Wavelet Galerkin Schemes for 2D-BEM

Abstract: This paper is concerned with the implementation of the wavelet Galerkin scheme for the Laplacian in two dimensions. We utilize biorthogonal wavelets constructed by A. Cohen, I. Daubechies and J.-C. Feauveau in [3] for the discretization leading to quasisparse system matrices which can be compressed without loss of accuracy. We develop algorithms for the computation of the compressed system matrices whose complexity is optimal, i.e., the complexity for assembling the system matrices in the wavelet basis is O(N J), where N J denotes the number of unknowns.

Biorthogonal nearly coiflet wavelets for image compression

Abstract: Filter bank design for wavelet compression is crucial; careful design enables superior quality for broad classes of images. The Bernstein basis for frequency-domain construction of biorthogonal nearly coiflet (BNC) wavelet bases forms a unified design framework for high-performance medium-length filters. A common filter bandwidth is characteristic of widely favoured BNC filter pairs: the classical CDF 9/7, the Villasenor 6/10, and the Villasenor 10/18. Based on this observation, we construct previously unknown BNC 17/11 and BNC 16/8 wavelet filters. Key filter-quality evaluation metrics, due to Villasenor, demonstrate these filters to be well suited for image compression. Also studied are the biorthogonal coiflet 17/11 (half-band), 18/10 and 10/6 filter pairs, which have not previously been formally evaluated for image coding. Simulation results confirm that the BNC 17/11 and BNC 16/8 wavelet bases are outstanding for compression of natural and medical images, and particularly for images with significant high-frequency detail, such as fingerprints. The BNC 17/11 pair recommends itself for international standardization for the compression of still images; the BNC 16/8 pair for high-quality compression of production quality video. Experimental evidence suggests biorthogonal filters achieve good compression if, subject to a filter bandwidth constraint, maximum vanishing moments are obtained for a given filter support.

Random field representation in a biorthogonal wavelet basis

Abstract: This paper develops a new representation scheme for random fields, which can be used in a variety of mechanics applications, based upon the projection onto a biorthogonal wavelet basis. The merits of such a scheme can be shown to result from the relaxation of the condition of orthonormality, while still requiring compact support of the basis functions. Earlier methods have relied on the diagonalization properties of wavelets to demonstrate how the Daubechies family of orthonormal wavelets is effective in weakening the correlation across scales for a large class of random processes. It is shown that biorthogonal processes achieve better decorrelation owing to the fact that fewer filter coefficients are needed to maintain the same support of basis functions when compared to the Daubechies family. Numerical examples of fields encountered in earthquake engineering and other applications are given.

Biorthogonal Butterworth wavelets derived from discrete interpolatory splines

Abstract: We present a new family of biorthogonal wavelet transforms and a related library of biorthogonal periodic symmetric waveforms. For the construction, we used the interpolatory discrete splines, which enabled us to design a library of perfect reconstruction filterbanks. These filterbanks are related to Butterworth filters. The construction is performed in a "lifting" manner. The difference from the conventional lifting scheme is that all the transforms are implemented in the frequency domain with the use of the fast Fourier transform (FFT). Two ways to choose the control filters are suggested. The proposed scheme is based on interpolation, and as such, it involves only samples of signals, and it does not require any use of quadrature formulas. These filters have a linear-phase property, and the basic waveforms are symmetric. In addition, these filters yield refined frequency resolution.

Biorthogonal Wavelet Based Identification of Fast Linear Time-Varying Systems—Part I: System Representations12

Abstract: An analytical framework is developed that permits the input-output representations of discrete-time linear time-varying (LTV) systems in terms of biorthogonal bases on compact time intervals. Using these representations, the companion paper, Part II develops computational procedures for rapid identification of fast nonsmooth LTV systems based on short data records. One of the representations proposed is also used in H. Zhao and J. Bentsman, "Block Diagram Reduction of the Interconnected Linear Time-Varying Systems in the Time Frequency Domain," " accepted for publication by Multidimensional Systems and Signal Processing to form system interconnections, or wavelet networks, and develop subsystem connectibility conditions and reduction rules. Under the assumption that the inputs and the outputs of the plants considered in the present work belong to l p spaces, where p =2 or p = ∞ , their impulse responses are shown to belong to Banach spaces. Further on, by demonstrating that the set of all bounded-input bounded-output (BIBO) stable discrete-time LTV systems is a Banach space, the system representation problem is shown to be reducible to the linear approximation problem in the Banach space setting, with the approximation errors converging to zero as the number of terms in the representation increases. Three types of LTV system representation, based on the input-side, the output-side, and the input-output transformations, are developed and the suitability of each representation for matching a particular type of the LTV system behavior is indicated.

Boundary filter optimization for segmentation-based subband coding

Abstract: This paper presents boundary optimization techniques for the nonexpansive decomposition of arbitrary-length signals with multirate filterbanks. Both biorthogonal and paraunitary filterbanks are considered. The paper shows how matching moments and orthonormality can be imposed as additional conditions during the boundary filter optimization process. It provides direct solutions to the problem of finding good boundary filters for the following cases: (a) biorthogonal boundary filters with exactly matching moments and (b) orthonormal boundary filters with almost matching moments. With the proposed methods, numerical optimization is only needed if orthonormality and exactly matching moments are demanded. The proposed direct solutions are applicable to systems with a large number of subbands and/or very long filter impulse responses. Design examples show that the methods allow the design of boundary filters with good frequency selectivity.

Audio Effects Based on Biorthogonal Time-Varying Frequency Warping

Abstract: We illustrate the mathematical background and musical use of a class of audio effects based on frequency warping These effects alter the frequency content of a signal via spectral mapping They can be implemented in dispersive tapped delay lines based on a chain of all-pass filters In a homogeneous line with first-order all-pass sections, the signal formed by the output samples at a given time is related to the input via the Laguerre transform However, most musical signals require a time-varying frequency modification in order to be properly processed Vibrato in musical instruments or voice intonation in the case of vocal sounds may be modeled as small and slow pitch variations Simulation of these effects requires techniques for time-varying pitch and/or brightness modification that are very useful for sound processing The basis for time-varying frequency warping is a time-varying version of the Laguerre transformation The corresponding implementation structure is obtained as a dispersive tapped delay line, where each of the frequency dependent delay element has its own phase response Thus, time-varying warping results in a space-varying, inhomogeneous, propagation structure We show that time-varying frequency warping is associated to an expansion over biorthogonal sets generalizing the discrete Laguerre basis Slow time-varying characteristics lead to slowly varying parameter sequences The corresponding sound transformation does not suffer from discontinuities typical of delay lines based on unit delays

Rapid prototyping of biorthogonal discrete wavelet transforms on FPGAs

Abstract: The purpose of this paper is to present a methodology for rapid prototyping of biorthogonal wavelet transforms on FPGAs. The methodology is based on adequate partitioning of a time interleaved "wait cycles" free architecture. The design has been captured using a schematic capture tools and can be parameterised in terms of the number of filter coefficients, data and coefficient word-lengths, digit size and degree of pipelining. The efficiency of the approach has been verified on the Xilinx 4000 FPGA series.

Video encoding method based on a wavelet decomposition

Abstract: The invention relates to a method for encoding a video sequence subdivided into groups of frames. This method comprises an on-line procedure in which a three-dimensional wavelet decomposition is performed involving a biorthogonal filter bank in a lifting scheme using optimal weighting constants. These constants are determined thanks to an additional off-line procedure in which a similar decomposition is performed but without any weighting constants.