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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01 Jan 2009
TL;DR: Comparisons show the superior performance of the symmetric biorthogonal wavelets in the presence of noisy images and changing lighting conditions when compared to the application of high order Daubechies wavelets.
Abstract: Moving object detection is a fundamental task for a variety of traffic applications. In this paper the Daubechies and biorthogonal wavelet families are exploited for extracting the relevant movement information in moving image sequences in a 3D wavelet-based segmentation algorithm. The proposed algorithm is applied for traffic monitoring systems. The objective and subjective experimental results obtained by applying both wavelet types are compared and interpreted in terms of the different wavelet properties and the characteristics of the image sequences. The comparisons show the superior performance of the symmetric biorthogonal wavelets in the presence of noisy images and changing lighting conditions when compared to the application of high order Daubechies wavelets. The algorithm is evaluated using simulated images in the Matlab environment.
20 citations
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TL;DR: In this paper, the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) in quasi-Banach spaces is studied from a functional-analytic point of view.
Abstract: The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) in quasi-Banach spaces from a functional-analytic point of view. We revisit the concepts of greedy, quasi-greedy, and almost greedy bases in this comprehensive framework and provide the (nontrivial) extensions of the corresponding characterizations of those types of bases. As a by-product of our work, new properties arise, and the relations amongst them are carefully discussed.
19 citations
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TL;DR: In this paper, the authors derived sampling theorems associated with q-biorthogonal systems and derived interpolation expansions for qHankel transforms whose kernels are the second-type q-Bessel functions J (2) ν (z; q), ν > 0,0
Abstract: This paper deals with the derivation of sampling theorems associated with q-biorthogonal systems. We derive interpolation expansions for qHankel transforms whose kernels are the second-type q-Bessel functions J (2) ν (z; q), ν > 0,0
19 citations
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TL;DR: In this paper, a sampling theorem-based approach to the eigenvalue problem associated with bandlimited integral kernels of convolution type is described, and two sets of functions biorthogonal to eigen functions are constructed and several identities satisfied by them are derived.
Abstract: We describe a novel approach based on the sampling theorem for studying eigenvalue problems associated with bandlimited integral kernels of convolution type. Two sets of functions biorthogonal to the eigenfunctions, one over the infinite interval and the other over a finite interval, are constructed and several identities satisfied by them are derived. The sampling theorem-based approach to the eigenvalue problem is further extended to construct the singular functions associated with the integral operator. It is shown that for the special case of the sinc-kernel, the eigenfunctions, the two biorthogonal sets and the singular functions reduce to the angular prolate spheroidal functions (or Slepian functions). Two methods are discussed for treating the inverse problem associated with bandlimited kernels—one employing the eigenfunctions and the biorthogonal sets and the other employing the singular functions. Numerical examples are included to illustrate the computation of eigenfunctions, biorthogonal sets and the singular functions and their application to the estimation of inverse solution.
19 citations
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01 Jan 2001TL;DR: In this article, the authors used biorthogonal wavelets constructed by A. Cohen, I. Daubechies and J.-C. Feauveau in [3] for discretization leading to quasisparse system matrices which can be compressed without loss of accuracy.
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.
19 citations