Journal of Computational Physics, ISSN 0021-9991, 05/2017, Volume 337, pp. 42 - 61

In this paper, we present a fast time adaptive numerical method for interface tracking. The method uses an explicit multiresolution description of the...

Adaptive methods | Interface tracking | Multiresolution analysis | Fast algorithms | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TRAVEL-TIME | REGULARITY | PHYSICS, MATHEMATICAL | 2-SCALE DIFFERENCE-EQUATIONS | Analysis | Methods | Numerical analysis | Usage | Algorithms

Adaptive methods | Interface tracking | Multiresolution analysis | Fast algorithms | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | TRAVEL-TIME | REGULARITY | PHYSICS, MATHEMATICAL | 2-SCALE DIFFERENCE-EQUATIONS | Analysis | Methods | Numerical analysis | Usage | Algorithms

Journal Article

Sbornik: Mathematics, ISSN 1064-5616, 10/2006, Volume 197, Issue 9-10, pp. 1529 - 1558

For an arbitrary positive integer n refinable functions on the positive half-line, R+ are defined, with masks that are Walsh polynomials of order 2(n) - 1. The...

MATHEMATICS | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS

MATHEMATICS | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS

Journal Article

SIAM journal on mathematical analysis, ISSN 1095-7154, 1998, Volume 29, Issue 2, pp. 511 - 546

We present the lifting scheme, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one...

Wavelet | Second generation wavelet | Lifting scheme | Multiresolution | MULTIRESOLUTION ANALYSES | MATHEMATICS, APPLIED | COMPACTLY SUPPORTED WAVELETS | ORTHONORMAL BASES | SPACES | second generation wavelet | REPRESENTATION | DECOMPOSITION | lifting scheme | 2-SCALE DIFFERENCE-EQUATIONS | SPLINE WAVELETS | FILTER BANKS | wavelet | multiresolution | SCALING FUNCTIONS

Wavelet | Second generation wavelet | Lifting scheme | Multiresolution | MULTIRESOLUTION ANALYSES | MATHEMATICS, APPLIED | COMPACTLY SUPPORTED WAVELETS | ORTHONORMAL BASES | SPACES | second generation wavelet | REPRESENTATION | DECOMPOSITION | lifting scheme | 2-SCALE DIFFERENCE-EQUATIONS | SPLINE WAVELETS | FILTER BANKS | wavelet | multiresolution | SCALING FUNCTIONS

Journal Article

Reviews of geophysics (1985), ISSN 8755-1209, 1997, Volume 35, Issue 4, pp. 385 - 412

Wavelet transforms originated in geophysics in the early 1980s for the analysis of seismic signals. Since then, significant mathematical advances in wavelet...

GEOCHEMISTRY & GEOPHYSICS | FOREST CANOPY | TURBULENT COHERENT MOTIONS | MULTICOMPONENT DECOMPOSITION | FRACTIONAL BROWNIAN-MOTION | SAMPLING THEORY | SIGNAL ANALYSIS | REPRESENTATION | SPATIAL RAINFALL FIELDS | 2-SCALE DIFFERENCE-EQUATIONS | TRANSFORMS

GEOCHEMISTRY & GEOPHYSICS | FOREST CANOPY | TURBULENT COHERENT MOTIONS | MULTICOMPONENT DECOMPOSITION | FRACTIONAL BROWNIAN-MOTION | SAMPLING THEORY | SIGNAL ANALYSIS | REPRESENTATION | SPATIAL RAINFALL FIELDS | 2-SCALE DIFFERENCE-EQUATIONS | TRANSFORMS

Journal Article

Discrete and Continuous Dynamical Systems, ISSN 1078-0947, 03/2008, Volume 20, Issue 3, pp. 639 - 657

The topological pressure is defined for sub-additive potentials via separated sets and open covers in general compact dynamical systems. A variational...

Thermodynamical formalism | Entropy | Topological pressure | Lyapunov exponents | Products of matrices | Variational principle | HAUSDORFF DIMENSION | MATHEMATICS, APPLIED | NONNEGATIVE MATRICES | 2-SCALE DIFFERENCE-EQUATIONS | thermodynamical formalism | MATHEMATICS | variational principle | PRESSURE | FRACTALS | entropy | PRODUCTS | REGULARITY | products of matrices | SYSTEMS | topological pressure

Thermodynamical formalism | Entropy | Topological pressure | Lyapunov exponents | Products of matrices | Variational principle | HAUSDORFF DIMENSION | MATHEMATICS, APPLIED | NONNEGATIVE MATRICES | 2-SCALE DIFFERENCE-EQUATIONS | thermodynamical formalism | MATHEMATICS | variational principle | PRESSURE | FRACTALS | entropy | PRODUCTS | REGULARITY | products of matrices | SYSTEMS | topological pressure

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 04/2014, Volume 287, Issue 5-6, pp. 546 - 560

It is known that there is no orthonormal wavelet belonging to C∞ and having exponential decay. In this paper, we shall construct new wavelets having Gevrey...

subexponential decay | Wavelets | Gevrey class | 46E10 | 42C40 | Subexponential decay | MATHEMATICS | BAND-LIMITED WAVELETS | 2-SCALE DIFFERENCE-EQUATIONS

subexponential decay | Wavelets | Gevrey class | 46E10 | 42C40 | Subexponential decay | MATHEMATICS | BAND-LIMITED WAVELETS | 2-SCALE DIFFERENCE-EQUATIONS

Journal Article

Applied and computational harmonic analysis, ISSN 1063-5203, 2003, Volume 15, Issue 2, pp. 89 - 116

We analyze the convergence and smoothness of certain class of nonlinear subdivision schemes. We study the stability properties of these schemes and apply this...

MATHEMATICS, APPLIED | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS

MATHEMATICS, APPLIED | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS

Journal Article

Numerische Mathematik, ISSN 0029-599X, 10/2014, Volume 128, Issue 2, pp. 339 - 375

Fast high order methods for the propagation of an interface in a velocity field are constructed and analyzed. The methods are generalizations of the fast...

Mathematical Methods in Physics | 42C40 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | 65D99 | Numerical and Computational Physics | Mathematics, general | 65L20 | Mathematics | MATHEMATICS, APPLIED | SUBDIVISION SCHEMES | TRAVEL-TIME | SMOOTHNESS | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS

Mathematical Methods in Physics | 42C40 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | 65D99 | Numerical and Computational Physics | Mathematics, general | 65L20 | Mathematics | MATHEMATICS, APPLIED | SUBDIVISION SCHEMES | TRAVEL-TIME | SMOOTHNESS | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 09/2014, Volume 548, Issue C, pp. 25 - 53

Among all sequences that satisfy a divide-and-conquer recurrence, those which are rational with respect to a numeration system are certainly the most basic and...

Cascade algorithm | Dilation equation | Divide-and-conquer recurrence | Spectral radius | Dirichlet series | Radix-rational sequence | Fourier series | NUMBER | BEHAVIOR | ALGORITHM | JOINT SPECTRAL-RADIUS | DIGITAL SUMS | 2-SCALE DIFFERENCE-EQUATIONS | REGULARITY | MATRICES | MELLIN TRANSFORMS | COMPUTER SCIENCE, THEORY & METHODS | Analysis | Algebra | Asymptotic expansions | Periodic functions | Asymptotic properties | Mathematical analysis | Linear algebra | Recall | Computer Science | Computational Complexity

Cascade algorithm | Dilation equation | Divide-and-conquer recurrence | Spectral radius | Dirichlet series | Radix-rational sequence | Fourier series | NUMBER | BEHAVIOR | ALGORITHM | JOINT SPECTRAL-RADIUS | DIGITAL SUMS | 2-SCALE DIFFERENCE-EQUATIONS | REGULARITY | MATRICES | MELLIN TRANSFORMS | COMPUTER SCIENCE, THEORY & METHODS | Analysis | Algebra | Asymptotic expansions | Periodic functions | Asymptotic properties | Mathematical analysis | Linear algebra | Recall | Computer Science | Computational Complexity

Journal Article

10.
Full Text
Fast FIR Algorithms for the Continuous Wavelet Transform From Constrained Least Squares

IEEE Transactions on Signal Processing, ISSN 1053-587X, 01/2013, Volume 61, Issue 1, pp. 28 - 37

New algorithms for the continuous wavelet transform are developed that are easy to apply, each consisting of a single-pass finite impulse response (FIR)...

Algorithm design and analysis | Continuous wavelet transforms | Filter banks | Finite impulse response filter | signal processing algorithms | Filtering theory | Discrete wavelet transforms | finite impulse response filter | continuous wavelet transforms | DESIGN | REPRESENTATION | 2-SCALE DIFFERENCE-EQUATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | MULTIRESOLUTION | DECOMPOSITIONS | REGULARITY | DISCRETE | FILTER BANKS | COMPUTATION | INITIALIZATION | Wavelet transforms | Signal processing | Usage | Least squares | Innovations | Wavelet | Algorithms | Least squares method | Mathematical analysis | Continuous wavelet transform | Impulse response | Transaction processing

Algorithm design and analysis | Continuous wavelet transforms | Filter banks | Finite impulse response filter | signal processing algorithms | Filtering theory | Discrete wavelet transforms | finite impulse response filter | continuous wavelet transforms | DESIGN | REPRESENTATION | 2-SCALE DIFFERENCE-EQUATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | MULTIRESOLUTION | DECOMPOSITIONS | REGULARITY | DISCRETE | FILTER BANKS | COMPUTATION | INITIALIZATION | Wavelet transforms | Signal processing | Usage | Least squares | Innovations | Wavelet | Algorithms | Least squares method | Mathematical analysis | Continuous wavelet transform | Impulse response | Transaction processing

Journal Article

IEEE transactions on image processing, ISSN 1057-7149, 2003, Volume 12, Issue 9, pp. 1080 - 1090

The LeGall 5/3 and Daubechies 9/7 filters have risen to special prominence because they were selected for inclusion in the JPEG2000 standard. We determine...

Wavelet transforms | Image quality | Image coding | Transform coding | Filter bank | Performance loss | Performance analysis | Decoding | Discrete cosine transforms | Spline | APPROXIMATION TECHNIQUES | QUANTITATIVE FOURIER-ANALYSIS | COMPACTLY SUPPORTED WAVELETS | REGULARITY | EXPANSIONS | CONSTRUCTION | INTERPOLATORS | BIORTHOGONAL WAVELETS | IMAGE COMPRESSION | 2-SCALE DIFFERENCE-EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Image processing | Data compression | Research | Wavelet | Error analysis | Approximation | Asymptotic properties | Mathematical analysis | Projection | Standards | Stands

Wavelet transforms | Image quality | Image coding | Transform coding | Filter bank | Performance loss | Performance analysis | Decoding | Discrete cosine transforms | Spline | APPROXIMATION TECHNIQUES | QUANTITATIVE FOURIER-ANALYSIS | COMPACTLY SUPPORTED WAVELETS | REGULARITY | EXPANSIONS | CONSTRUCTION | INTERPOLATORS | BIORTHOGONAL WAVELETS | IMAGE COMPRESSION | 2-SCALE DIFFERENCE-EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Image processing | Data compression | Research | Wavelet | Error analysis | Approximation | Asymptotic properties | Mathematical analysis | Projection | Standards | Stands

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 02/2003, Volume 51, Issue 2, pp. 470 - 483

We revisit wavelet theory starting from the representation of a scaling function as the convolution of a B-spline (the regular part of it) and a distribution...

Wavelet transforms | Filtering | Signal processing algorithms | Finite impulse response filter | Filter bank | Polynomials | Digital filters | Signal analysis | Image reconstruction | Spline | Wavelets | Splines | Approximation order | Hölder smoothness | Vanishing moments | Besov spaces | Multiscale differentiation | DILATION EQUATIONS | SIGNAL | SPLINE-WAVELETS | COMPACTLY SUPPORTED WAVELETS | ORTHONORMAL BASES | Holder smoothness | splines | 2-SCALE DIFFERENCE-EQUATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | multiscale differentiation | REGULARITY | wavelets | FILTER BANKS | vanishing moments | CONVERGENCE | approximation order | Electric filters | Signal processing | Research | Spline theory | Studies | Wavelet | Reproduction | Theorems | Basis functions | Derivatives | Representations | Smoothness

Wavelet transforms | Filtering | Signal processing algorithms | Finite impulse response filter | Filter bank | Polynomials | Digital filters | Signal analysis | Image reconstruction | Spline | Wavelets | Splines | Approximation order | Hölder smoothness | Vanishing moments | Besov spaces | Multiscale differentiation | DILATION EQUATIONS | SIGNAL | SPLINE-WAVELETS | COMPACTLY SUPPORTED WAVELETS | ORTHONORMAL BASES | Holder smoothness | splines | 2-SCALE DIFFERENCE-EQUATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | multiscale differentiation | REGULARITY | wavelets | FILTER BANKS | vanishing moments | CONVERGENCE | approximation order | Electric filters | Signal processing | Research | Spline theory | Studies | Wavelet | Reproduction | Theorems | Basis functions | Derivatives | Representations | Smoothness

Journal Article

International Journal of Wavelets, Multiresolution and Information Processing, ISSN 0219-6913, 01/2018, Volume 16, Issue 1

The area of nonlinear time series models has experienced a great development since the 1980s. Although there is a wide range of parametric nonlinear time...

varying coefficient models | Daubechies-Lagarias algorithm | functional autoregressive models | warped wavelets | father wavelets | DENSITY-ESTIMATION | NONPARAMETRIC REGRESSION | 2-SCALE DIFFERENCE-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SHRINKAGE | REGULARITY | DIMENSION | TIME-SERIES | RANDOM DESIGN

varying coefficient models | Daubechies-Lagarias algorithm | functional autoregressive models | warped wavelets | father wavelets | DENSITY-ESTIMATION | NONPARAMETRIC REGRESSION | 2-SCALE DIFFERENCE-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SHRINKAGE | REGULARITY | DIMENSION | TIME-SERIES | RANDOM DESIGN

Journal Article

Constructive approximation, ISSN 1432-0940, 2004, Volume 20, Issue 3, pp. 399 - 463

A multiresolution analysis of a curve is normal if each wavelet detail vector with respect to a certain subdivision scheme lies in the local normal direction....

Wavelet | Subdivision | Normal mesh | Normal multiresolution | Lifting | Philosophy | MATHEMATICS | subdivision | normal mesh | normal multiresolution | REGULARITY | lifting | wavelet | 2-SCALE DIFFERENCE-EQUATIONS

Wavelet | Subdivision | Normal mesh | Normal multiresolution | Lifting | Philosophy | MATHEMATICS | subdivision | normal mesh | normal multiresolution | REGULARITY | lifting | wavelet | 2-SCALE DIFFERENCE-EQUATIONS

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 03/2013, Volume 438, Issue 5, pp. 2107 - 2126

Radix-rational sequences are solutions of systems of recurrence equations based on the radix representation of the index. For each radix-rational sequence with...

Dilation equation | Asymptotic analysis | Radix-rational sequence | Rational formal power series | Joint spectral radius | Self-similarity | MATHEMATICS, APPLIED | REGULARITY | MATRICES | MELLIN TRANSFORMS | 2-SCALE DIFFERENCE-EQUATIONS | Analysis | Algebra | Algorithms | Operator Algebras | Mathematics | Computer Science | Discrete Mathematics

Dilation equation | Asymptotic analysis | Radix-rational sequence | Rational formal power series | Joint spectral radius | Self-similarity | MATHEMATICS, APPLIED | REGULARITY | MATRICES | MELLIN TRANSFORMS | 2-SCALE DIFFERENCE-EQUATIONS | Analysis | Algebra | Algorithms | Operator Algebras | Mathematics | Computer Science | Discrete Mathematics

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2008, Volume 56, Issue 7, pp. 1845 - 1851

An algorithm for constructing a pair of biorthogonal two-direction refinable function and the corresponding biorthogonal two-direction wavelet is presented. In...

Two-direction refinable function | Two-direction wavelet | Biorthogonal | Dilation factor | MATHEMATICS, APPLIED | two-direction refinable function | REGULARITY | two-direction wavelet | biorthogonal | dilation factor | 2-SCALE DIFFERENCE-EQUATIONS | Algorithms | Wavelet | Dilation | Construction | Mathematical models | Mathematical analysis

Two-direction refinable function | Two-direction wavelet | Biorthogonal | Dilation factor | MATHEMATICS, APPLIED | two-direction refinable function | REGULARITY | two-direction wavelet | biorthogonal | dilation factor | 2-SCALE DIFFERENCE-EQUATIONS | Algorithms | Wavelet | Dilation | Construction | Mathematical models | Mathematical analysis

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 207, Issue 1, pp. 83 - 89

The concept of general two-scale similarity transform (GTST) is introduced. By applying GTST, we present an algorithm of constructing a class of balanced...

Balanced order | Refinable function vector | GTST | Symmetry | EXISTENCE | MATHEMATICS, APPLIED | DESIGN | MULTISCALING FUNCTIONS | MULTI-WAVELETS | 2-SCALE DIFFERENCE-EQUATIONS | REGULARITY | APPROXIMATION ORDER | MULTIWAVELETS | Algorithms

Balanced order | Refinable function vector | GTST | Symmetry | EXISTENCE | MATHEMATICS, APPLIED | DESIGN | MULTISCALING FUNCTIONS | MULTI-WAVELETS | 2-SCALE DIFFERENCE-EQUATIONS | REGULARITY | APPROXIMATION ORDER | MULTIWAVELETS | Algorithms

Journal Article

Comptes rendus - Mathématique, ISSN 1631-073X, 2004, Volume 338, Issue 4, pp. 321 - 326

The goal of this Note is to present some theoretical results for the nonlinear multiscales representations concerning the smoothness characterization through...

MATHEMATICS | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS

MATHEMATICS | REGULARITY | 2-SCALE DIFFERENCE-EQUATIONS

Journal Article

Izvestiya: Mathematics, ISSN 1064-5632, 10/2006, Volume 70, Issue 5, pp. 975 - 1013

We introduce the notion of a summable fractal curve generated by a finite family of affine operators. This generalizes well-known notions of affine fractals...

MATHEMATICS | REGULARITY | PRODUCTS | MATRICES | REFINEMENT EQUATIONS | JOINT SPECTRAL-RADIUS | SUBDIVISION SCHEMES | 2-SCALE DIFFERENCE-EQUATIONS

MATHEMATICS | REGULARITY | PRODUCTS | MATRICES | REFINEMENT EQUATIONS | JOINT SPECTRAL-RADIUS | SUBDIVISION SCHEMES | 2-SCALE DIFFERENCE-EQUATIONS

Journal Article

Energy Exploration & Exploitation, ISSN 0144-5987, 6/2012, Volume 30, Issue 3, pp. 417 - 433

Well logging is an important tool for the characterization of subsurface rocks, being commonly used in the study of reservoir geology. It is well known that...

Minimax | Information retrieval noise | Threshing | Lithology | Signal noise | White noise | Wavelet analysis | Information classification | Mathematical functions | Coefficients | Wavelet Denoising | Signal processing | Well logs | Geological Enhancement | Thresholding Function | REGULARITY | ENERGY & FUELS | DECOMPOSITION | 2-SCALE DIFFERENCE-EQUATIONS | Wavelet | Wavelet transforms | Algorithms | Geology | Noise reduction | Classification | Tools | Discrete Wavelet Transform

Minimax | Information retrieval noise | Threshing | Lithology | Signal noise | White noise | Wavelet analysis | Information classification | Mathematical functions | Coefficients | Wavelet Denoising | Signal processing | Well logs | Geological Enhancement | Thresholding Function | REGULARITY | ENERGY & FUELS | DECOMPOSITION | 2-SCALE DIFFERENCE-EQUATIONS | Wavelet | Wavelet transforms | Algorithms | Geology | Noise reduction | Classification | Tools | Discrete Wavelet Transform

Journal Article

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