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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TL;DR: In this paper, biorthogonal wavelets are constructed on nonuniform ��meshes and both primal and dual wavelets generate Riesz bases for the Sobolev spaces for (|s| < 3/2) and the primal side span standard Lagrange finite element spaces, respectively.
Abstract: In this paper, biorthogonal wavelets are constructed on nonuniform
meshes. Both primal and dual wavelets are
locally supported, continuous piecewise polynomials. The wavelets generate
Riesz bases for the Sobolev spaces (H
s
) for (|s| < 3/2). The
wavelets at the primal side span standard Lagrange finite element spaces.
45 citations
TL;DR: A general way for the construction of quinc unx interpolatory refinement masks associated with the quincunx lattice in R2 attain the optimal approximation order and smoothness order.
Abstract: We analyze the approximation and smoothness properties of quincunx fundamental refinable functions. In particular, we provide a general way for the construction of quincunx interpolatory refinement masks associated with the quincunx lattice in R2. Their corresponding quincunx fundamental refinable functions attain the optimal approximation order and smoothness order. In addition, these examples are minimally supported with symmetry. For two special families of such quincunx interpolatory masks, we prove that their symbols are nonnegative. Finally, a general way of constructing quincunx biorthogonal wavelets is presented. Several examples of quincunx interpolatory masks and quincunx biorthogonal wavelets are explicitly computed.
45 citations
21 Apr 1997
TL;DR: Two new lapped transforms are introduced: the LBT (lapped biorthogonal transform) and the HLBT (hierarchical lapped bizonal transform), which have a significantly lower computational complexity than the LOT, essentially no blocking artifacts, and less ringing artifacts than the commonly-used DCT.
Abstract: Two new lapped transforms are introduced: the LBT (lapped biorthogonal transform) and the HLBT (hierarchical lapped biorthogonal transform). The LBT has the same computational complexity of the LOT (lapped orthogonal transform), with much less blocking artifacts. The HLBT has a significantly lower computational complexity than the LOT, essentially no blocking artifacts, and less ringing artifacts than the commonly-used DCT (discrete cosine transform). The LBT and HLBT have a transform coding gain that is typically between 0.5 and 2.5 dB higher than that of the DCT. Image coding examples using JPEG and embedded zerotree coders demonstrate the better performance of the LBT and HLBT.
45 citations
Book•
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01 Jan 1999
TL;DR: In this article, the authors proposed a method for the construction of exactly supported affine frames in L2 (IRd) and showed that these frames can be used to detect seizure.
Abstract: Frames, Sampling and Seizure Prediction (J. J. Benedetto).- Construction of Compactly Supported Affine Frames in L2 (IRd) (A. Ron & Z. Shen).- Understanding Wavelet Image Coding (S. Mallat & F. Falzon).- Multiplication of Short Wavelet Series using Connection Coefficients (V. Perrier & M. V. Wikckerhauser).- Conjugate Quadrature Filters (W. M. Lawton).- Polynomial Reproduction by Refinable Functions (C. A. Cabrelli et al.).- From Cardinal Hermite Splines to Multiwavelets (S. S Gog et al.).- Orthogonal Multiwavelet Constructions: 101 Things to do with a Hat Function (G. C. Donovan et al.).- Convergence of Vector Subdivision Schemes and Construction of Biorthogonal Multiple Wavelets (R. Q. Jia).- Study of Linear Independence and Accuracy of Scaling Vectors via Two-scale Factors (J. Z. Wang).- Self-Affine Tiles (Y. Wang).
45 citations
44 citations