Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.

Fast parametrized biorthogonal transforms

Abstract: In this paper the authors propose the buildling scheme of fast parametrized biorthogonal transforms taking advantage of data-flow graphs for calculation of fast orthonormal transforms and two-point biorthogonal butterfly operators. Streszczenie. W pracy zaproponowano schemat budowy szybkich parametryzowanych przeksztalce ´ n biortogonalnych oparty o diagramy przeply- wowe dla szybkich przeksztalce ´ n ortonormalnych i dwupunktowe biortogonalne operatory motylkowe. ( Szybkie parametryzowane transformacje bi-ortogonalne)

Discrete probability density estimation using multirate DSP models

Abstract: We propose a model based approach for estimation of probability mass functions for discrete random variables. The model is based on tools from multirate signal processing. Similar in principle to the kernel based methods, the approach takes advantage of well-known results from multirate signal processing theory. Similarities to and differences from wavelet based approaches are also indicated where appropriate. In the final form, the probability estimates are obtained by filtering the square root of the histogram through a multirate system whose components are biorthogonal partners of each other.

Multi-Scale Symmetry Transform with Application to Location of Feature Points on Human Face Image

Abstract: A method to implement multi scale symmetry transform in the wavelet coefficients domain decomposed by using anti symmetrical biorthogonal wavelets (ASBW) is presented with application to location of feature points on human face image.Compared to the original symmetry transform,which is performed on a single resolution level,our method can yield results with higher location accuracy without increment of computational burden.In addition,if an image is compressed based on ASBW decomposition,then our method provides a way to extract image features in compressed data domain without need of completely reconstructing the image.This is one of the most important technical consideration in the content based indexing (CBI) problem.

Nonharmonic Fourier series and spectral theory

Abstract: We consider the problem of using functions g" (x) exp (iX,1 x) to form biorthogonal expansions in the spaces LP(-7r, sr), for various values of p. The work of Paley and Wiener and of Levinson considered conditions of the form IX,, nI < A (p) which insure that {g,,} is part of a biorthogonal system and the resulting biorthogonal expansions are pointwise equiconvergent with ordinary Fourier series. Norm convergence is obtained for p = 2. In this paper, rather than imposing an explicit growth condition, we assume that { X, n } is a multiplier sequence on LP (-T, 7T). Conditions are given insuring that { g,, } inherits both norm and pointwise convergence properties of ordinary Fourier series. Further, Xn and gn are shown to be the eigenvalues and eigenfunctions of an unbounded operator A which is closely related to a differential operator, i A generates a strongly continuous group and -A2 generates a strongly continuous semigroup. Half-range expansions, involving cos X, x or sin X n x on (0, 7T) are also shown to arise from linear operators which generate semigroups. Many of these results are obtained using the functional calculus for well-bounded operators.

Biorthogonal Wavelet Transforms and Applications Based on Generalized Progressive Catmull-Clark Subdivision with Shape Control

Abstract: In recent years, some biorthogonal Catmull-Clark subdivision wavelet transforms constructed via the lifting scheme have been proposed to speed up processing of geometric models. Thanks to the idea of progressive interpolation, the compression qualities and noise-filtering effects have been improved significantly. However, the reconstruction precision fails to be improved further because many model details are removed and the noise-filtering performance decreases greatly while the noise intensity increases gradually. To deal with this dilemma, a unified Catmull-Clark subdivision based biorthogonal wavelet construction with shape control parameters is presented to process 3D models with sharp-feature constraints. By customizing its local orthogonalizing coefficients for different vertex valences of quadrilateral patches, the novel scheme can greatly strengthen the capability of the model's shape control that is vital for data compression, noise-filtering, etc. Combined with the local and in-place lifting operations, the proposed wavelet transform can dramatically decrease the memory consumption and computation complexity. Both theoretical analysis and numerical experiments show that, compared with the state-of-the-art lifting-based solutions, the proposed wavelet transform achieves higher compression ratio, more stable noise-filtering effects and better progressive transmission quality, not only decreasing the Bits/vertex of 3D meshes and improving the PSNR of reconstructed models, but also reducing the time costs of coding and decoding.