Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
Papers published on a yearly basis
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TL;DR: In this article, a general method for constructing a set of nonorthogonal bases with equal separations between all different basis states in prime dimensions was developed, and the corresponding biorthogonal counterparts are pairwise unbiased with the components of the original bases.
Abstract: We have developed a general method for constructing a set of nonorthogonal bases with equal separations between all different basis states in prime dimensions. The results are that the corresponding biorthogonal counterparts are pairwise unbiased with the components of the original bases. Using these bases, we derive an explicit expression for the optimal tomography in nonorthogonal bases. A special two-dimensional case is analyzed separately.
11 citations
02 Sep 2001
TL;DR: The purpose of this paper is to present a methodology for rapid prototyping of biorthogonal wavelet transforms on FPGAs based on adequate partitioning of a time interleaved "wait cycles" free architecture.
Abstract: The purpose of this paper is to present a methodology for rapid prototyping of biorthogonal wavelet transforms on FPGAs. The methodology is based on adequate partitioning of a time interleaved "wait cycles" free architecture. The design has been captured using a schematic capture tools and can be parameterised in terms of the number of filter coefficients, data and coefficient word-lengths, digit size and degree of pipelining. The efficiency of the approach has been verified on the Xilinx 4000 FPGA series.
11 citations
TL;DR: In this paper, a unified algorithm was developed to systematize the collection of compact Daubechies wavelets computable by spectral factorization of a symmetric positive polynomial.
11 citations
TL;DR: In this paper, the authors discuss notions of convolutions generated by biorthogonal systems of elements of a Hilbert space and discuss properties of convolution and give a number of examples.
Abstract: In this note we discuss notions of convolutions generated by biorthogonal systems of elements of a Hilbert space. We develop the associated biorthogonal Fourier analysis and the theory of distributions, discuss properties of convolutions and give a number of examples.
11 citations
Patent•
23 Jul 2001TL;DR: In this paper, a method for encoding a video sequence subdivided into groups of frames was proposed, which comprises an on-line procedure in which a three-dimensional wavelet decomposition is performed involving a biorthogonal filter bank in a lifting scheme using optimal weighting constants.
Abstract: The invention relates to a method for encoding a video sequence subdivided into groups of frames. This method comprises an on-line procedure in which a three-dimensional wavelet decomposition is performed involving a biorthogonal filter bank in a lifting scheme using optimal weighting constants. These constants are determined thanks to an additional off-line procedure in which a similar decomposition is performed but without any weighting constants.
11 citations