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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Dissertation•
09 Jul 2004
13 citations
Posted Content•
TL;DR: A backward biorthogonalization approach is proposed, which modifies biorhogonal functions so as to generate orthogonal projections onto a reduced subspace, relevant to problems amenable to be represented by a general linear model.
Abstract: A backward biorthogonalization approach is proposed, which modifies biorthogonal functions so as to generate orthogonal projections onto a reduced subspace. The technique is relevant to problems amenable to be represented by a general linear model. In particular, problems of data compression, noise reduction and sparse representations may be tackled by the proposed approach.
13 citations
TL;DR: In this paper, a numerical method for approximating the solution of the nonlinear Volterra integro-differential equation is presented, following a fixed-point approach, due to some properties of certain biorthogonal systems.
Abstract: This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .
13 citations
12 May 1998
TL;DR: A previously unpublished nearly coiflet 17/11 biorthogonal wavelet filter pair is constructed, and Simulation results with the SPIHT algorithm confirm that the new 17/ 11 wavelet basis outperforms the others for still image compression.
Abstract: The selection of the filter bank in wavelet compression is crucial, affecting the image quality and system design. The biorthogonal coiflet (cooklet) family of wavelet filters has been constructed, and explicit frequency domain formulae have been developed in the Bernstein polynomial basis. We use the Bernstein basis for the frequency domain design and construction of biorthogonal nearly coiflet wavelet bases. In particular, we construct a previously unpublished nearly coiflet 17/11 biorthogonal wavelet filter pair. Key filter quality evaluation metrics due to Villasenor (see IEEE Trans. on Image Proc., vol.4, no.8, p.1053-1060, 1995) demonstrate this filter pair to be well suited for image compression. Comparison is made to the 17/11 biorthogonal coiflet (cooklet), Villasenor 10/18, Odegard 9/7, and classical CDF 9/7 wavelet bases. Simulation results with the SPIHT algorithm due to Said and Pearlman (see IEEE Trans. on Circ. and Systems, vol.6, no.3, p.243-250, 1996), and with our SR/sub SFQ/, confirm that the new 17/11 wavelet basis outperforms the others for still image compression.
12 citations
TL;DR: Biorthogonal Fourier series occur when applying separation of variables to many problems and an approach which possesses considerable advantages with respect to the standard one is explained.
Abstract: Biorthogonal Fourier series occur when applying separation of variables to many problems. Here an approach which possesses considerable advantages with respect to the standard one is explained.
12 citations