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Biorthogonal system

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


Papers
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Proceedings ArticleDOI
01 Jan 2000
TL;DR: A new iterative method based on a wavelet representation of the image using a biorthogonal spline wavelet basis implemented on an oversampled grid is proposed and applied to disparity-compensated stereoscopic image interpolation.
Abstract: We are concerned with the reconstruction of a regularly-sampled image based on irregularly-spaced samples thereof. We propose a new iterative method based on a wavelet representation of the image. For this representation we use a biorthogonal spline wavelet basis implemented on an oversampled grid. We apply the developed algorithm to disparity-compensated stereoscopic image interpolation. Under disparity compensation, the resulting sampling grids are irregular and require the irregular/regular interpolation. We show the experimental results on real-world images and we compare our results with other methods proposed in the literature.

19 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed a new representation for random fields, which can be used in a variety of mechanics applications, based upon the projection onto 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.

19 citations

Proceedings ArticleDOI
06 Sep 2000
TL;DR: In this article, the orthogonal (or biorthogonal) filters are implemented with an M-band wavelet-based system in a form of cosines modulated filters to configure a perfect reconstruction system.
Abstract: This paper presents work carried out on a multi-carrier code division multiple access (MC-CDMA) for a down-link cellular radio systems. The MC-CDMA system carries out energy spreading in all available sub-channels or in the frequency domain. It also performs multi-carrier modulation using a set of orthogonal (or biorthogonal) filters. The optimisation of these filters is done based on their time-frequency characteristics and depends also on the application. Here the biorthogonal filters are implemented with M-band wavelet-based system in a form of cosines modulated filters to configure a perfect reconstruction system. The simulation results show that this WB-MC-CDMA system suffers lower interchannel interference, thus making its response more robust against multipath fading and narrow band interference or jamming signal.

19 citations

Journal ArticleDOI
TL;DR: This work builds a new biorthogonal pair of multi-resolution analyses on the interval, by integration or differentiation, and uses both pairs to construct isotropic or anisotropic divergence-free wavelet bases on the hypercube.

18 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202329
2022105
202155
202058
201960