Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
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TL;DR: In this paper, the strengthened Cauchy-Buniakowski-Schwarz inequality is reviewed for one dimensional biorthogonal wavelets and a theorem is proposed for the bidimensional case, concerning order one spline-wavelets.
Abstract: Multilevel methods have been widely applied for the approximation of the solutions of the elliptic partial differential equations in the frame of finite element spaces and, recently, owing to the development of the wavelet theory, in wavelet spaces. It has been pointed out that the strengthened Cauchy-Buniakowski-Schwarz inequality is the main tool in the analysis of multilevel methods. In this paper, results on the strengthened Cauchy-Buniakowski-Schwarz inequality are reviewed for one dimensional biorthogonal wavelets and, as original contribution, a theorem is proposed for the bidimensional case, concerning order one spline-wavelets. Mathematics subject classification (2000): 26D07, 65T60.
6 citations
TL;DR: An axiomatic approach to biorthogonal multiresolution analyzes on bounded domains is presented and construction of wavelet analysis within the new framework is illustrated with the design of a basis specifically tailored to reduce the boundary artifacts induced by some wavelet transforms used in image processing.
Abstract: An axiomatic approach to biorthogonal multiresolution analyzes on bounded domains is presented. The intervalized multiresolution analysis (MRA) leads to a generalized framework within which one can construct biorthogonal wavelet transforms, including many constructions presented in the literature to date. The framework also leads naturally to algorithms for calculating and constraining pertinent properties of both the discrete filters and their corresponding continuous basis functions. Construction of wavelet analysis within the new framework is then illustrated with the design of a basis specifically tailored to reduce the boundary artifacts induced by some wavelet transforms used in image processing.
6 citations
TL;DR: In this article, the minimal hyperbolic splines and their properties are considered, and formulas for constructing quadratic splines, and corresponding biorthogonal (dual) functionals are obtained.
Abstract: The paper considers the minimal hyperbolic splines and their properties. Formulas for constructing quadratic splines and the corresponding biorthogonal (dual) functionals are obtained. Numerical results, demonstrating how approximation quality can be improved by using hyperbolic splines and changing control parameters, are presented.
6 citations
TL;DR: In this paper, the biorthogonal Appell system and Kondrat’ev spaces were studied in the case where the parameter of a μ-exponential is perturbed by holomorphic invertible functions.
Abstract: We study the biorthogonal Appell system and Kondrat’ev spaces in the case where the parameter of a μ-exponential is perturbed by holomorphic invertible functions. The results obtained are applied to the investigation of pseudodifferential equations.
6 citations
Patent•
08 Oct 2014
TL;DR: In this paper, a method for constructing a biorthogonal wavelet filter bank was proposed, which includes the following steps: determining the length N of a decomposition lowpass filter h(n) and the length M of a reconstruction low-pass filter (please see the specifications) according to the requirements of wavelet functions to be constructed, wherein the N and the M are even numbers.
Abstract: The invention discloses a method for constructing a biorthogonal wavelet filter bank. The method includes the following steps: determining the length N of a decomposition low-pass filter h(n) and the length M of a reconstruction low-pass filter (please see the specifications) according to the requirements of wavelet functions to be constructed, wherein the N and the M are even numbers; determining the orders of vanishing moments of dual wavelet generating functions (please see the specifications) to be constructed; calculating the biorthogonal complete reconstruction filter bank according to a formula set to obtain a set of coefficients of the biorthogonal complete reconstruction filter bank; substituting the results into a dual-scale equation to construct a set of biorthogonal wavelet bases (please see the specifications), decomposing a decomposition high-pass filter corresponding to the wavelet function (please see the specifications), and reconstructing a reconstruction high-pass filter corresponding to the wavelet function (please see the specifications). Compared with common db-series wavelet filter banks and common bior-series wavelet filter banks, heart sound signals are processed through the biorthogonal wavelet filter bank constructed with the method, and the better noise reduction effect, the accurate heart sound classified information and the smaller reconstruction error rate can be obtained.
6 citations