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
Papers
More filters
TL;DR: In this article, the authors studied the problem of computing the normalisations and the biorthogonal polynomials of the Muttalib-Borodin ensembles with classical weights on the positive half-line.
12 citations
TL;DR: It is shown that these wavelets of variable polynomial order up to four dimensions have a much sparser representation of discontinuous functions as compared to tensor product wavelets, which allows for a more compact and efficient representation.
12 citations
TL;DR: In this paper, the authors review some basic definitions and few facts recently established for pseudo bosons and pseudo-fermions and discuss an extended version of these latter, based on biorthogonal bases, which lives in a finite dimensional Hilbert space.
Abstract: We review some basic definitions and few facts recently established for $\D$-pseudo bosons and for pseudo-fermions. We also discuss an extended version of these latter, based on biorthogonal bases, which lives in a finite dimensional Hilbert space. Some examples are described in details.
12 citations
07 Aug 2002
TL;DR: In this article, a new family of lapped biorthogonal transform is introduced, called the IntLBT, which is implemented by a series of dyadic lifting steps and provides very fast, efficient in-place computation of the transform coefficients.
Abstract: By scaling all discrete cosine transform (DCT) intermediate output coefficients of the lapped transform and employing the type-II and type-IV DCT based on lifting steps, a new family of lapped biorthogonal transform is introduced, called the IntLBT. When all the elements with a floating point of each lifting matrix in the IntLBT are approximated by binary fractions, the IntLBT is implemented by a series of dyadic lifting steps and provides very fast, efficient in-place computation of the transform coefficients, and all internal nodes have finite precision. When each lifting step in the IntLBT is implemented using the same nonlinear operations as those used in the well known integer-to-integer wavelet transform, the IntLBT maps integers to integers, so it can express lossless image information. As an application of the novel IntLBT to lossy image compression, simulation results demonstrate that the IntLBT has significantly less blocking artefacts, higher peak signal-to-noise ratio, and better visual quality than the DCT. More importantly, the IntLBT's coding performance is approximately the same as that of the much more complex Cohen-Daubechies-Feauveau (CDF) 9/7-tap biorthogonal wavelet with floating-point coefficients, and in some cases even surpasses that of the CDF 9/7-tap biorthogonal wavelet.
12 citations
15 Apr 2007
TL;DR: This work proposes to further extend this framework on two fronts by considering biorthogonal and complex M-band dual-tree decompositions, andDenoising results are provided to demonstrate the validity of the proposed design rules.
Abstract: Dual-tree wavelet transforms have recently gained popularity since they provide low-redundancy directional analyses of images. In our recent work, dyadic real dual-tree decompositions have been extended to the M-band case, so adding much flexibility to this analysis tool. In this work, we propose to further extend this framework on two fronts by considering (i) biorthogonal and (ii) complex M-band dual-tree decompositions. Denoising results are finally provided to demonstrate the validity of the proposed design rules.
12 citations