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1.
Factoring wavelet transforms into lifting steps 总被引:236,自引:0,他引:236
This article is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with
finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are
also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet
or subband filters into elementary matrices. That such a factorization is possible is well-known to algebraists (and expressed
by the formulaSL(n;R[z, z−1])=E(n;R[z, z−1])); it is also used in linear systems theory in the electrical engineering community. We present here a self-contained derivation,
building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering.
This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the
biorthogonal, i.e., non-unitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces
the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining
a wavelet-like transform that maps integers to integers.
Research Tutorial
Acknowledgements and Notes. Page 264. 相似文献
2.
3.
A new polynomial-time algorithm for linear programming 总被引:116,自引:0,他引:116
N. Karmarkar 《Combinatorica》1984,4(4):373-395
We present a new polynomial-time algorithm for linear programming. In the worst case, the algorithm requiresO(n
3.5
L) arithmetic operations onO(L) bit numbers, wheren is the number of variables andL is the number of bits in the input. The running-time of this algorithm is better than the ellipsoid algorithm by a factor
ofO(n
2.5). We prove that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property. The ratio of the radius of the smallest sphere with center a′, containingP′ to the radius of the largest sphere with center a′ contained inP′ isO(n). The algorithm consists of repeated application of such projective transformations each followed by optimization over an
inscribed sphere to create a sequence of points which converges to the optimal solution in polynomial time.
This is a substantially revised version of the paper presented at the Symposium on Theory of Computing, Washington D. C.,
April 1984. 相似文献
4.
MV-代数、BL-代数、R0-代数与多值逻辑 总被引:91,自引:20,他引:71
证明三种不同形式的MV-代数刻画的等价性,分析MV-代数、BL-代数与R0代数的逻辑背景,提出若干可进一步研究的课题。 相似文献
5.
The ergodic theory of Markov chains in random environments 总被引:70,自引:0,他引:70
Robert Cogburn 《Probability Theory and Related Fields》1984,66(1):109-128
Summary A general formulation of the stochastic model for a Markov chain in a random environment is given, including an analysis of the dependence relations between the environmental process and the controlled Markov chain, in particular the problem of feedback. Assuming stationary environments, the ergodic theory of Markov processes is applied to give conditions for the existence of finite invariant measure (equilibrium distributions) and to obtain ergodic theorems, which provide results on convergence of products of random stochastic matrices. Coupling theory is used to obtain results on direct convergence of these products and the structure of the tail -field. State properties including classification and communication properties are discussed. 相似文献
6.
A nonsmooth version of Newton's method 总被引:69,自引:0,他引:69
Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian forC
2-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.This author's work is supported in part by the Australian Research Council.This author's work is supported in part by the National Science Foundation under grant DDM-8721709. 相似文献
7.
Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes 总被引:68,自引:0,他引:68
In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition K/hK c0 > 0 is not satisfied, wherehK is the diameter of the element K and K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L2-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek. 相似文献
8.
THE SINGULARLY PERTURBED PROBLEM FOR COMBUSTION REACTION DIFFUSION 总被引:65,自引:0,他引:65
莫嘉琪 《应用数学学报(英文版)》2001,17(2):255-259
1. IntroductionThe anchor discussed a class of problems for the nonlinear ordinary differential equations(of. [1-3]) and the reaction dimsion equations (of. [4-7]).Now we consider a model of the combustion reaction decision problem as follows:where y is a density of combustion flame, s denotes the rate of diffusion effect for reactionspeed, whiCh is a small positive parameter, t is a position of combustion, functions y - t andy t are the positions of the matter for fuel and chide respectivel… 相似文献
9.
The search for chromatically unique graphs 总被引:64,自引:0,他引:64
The number of vertex-colourings of a simple graphG in not more than colours is a polynomial in. This polynomial, denoted byP(G, ), is called the chromatic polynomial ofG. A graphG is said to be chromatically unique, in short-unique, ifH G for any graphH withP(H, ) = P(G, ). Since the appearance of the first paper on-unique graphs by Chao and Whitehead in 1978, various families of and several results on such graphs have been obtained successively, especially during the last five years. It is the aim of this expository paper to give a survey on most of the works done on-unique graphs. A number of related problems and conjectures are also included.1980 Mathematical Subject Classification. Primary 05C15This work was done while the author was visiting the Department of Mathematics, National University of Singapore. 相似文献
10.
A generalization of Tychonoff's fixed point theorem 总被引:59,自引:0,他引:59
Ky Fan 《Mathematische Annalen》1961,142(3):305-310