共查询到20条相似文献,搜索用时 15 毫秒
1.
Discrete Gabor structures and optimal representations 总被引:1,自引:0,他引:1
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The generalized Gabor transform (for image representation) is discussed. For a given function f(t), tinR, the generalized Gabor transform finds a set of coefficients a(mr) such that f(t)=Sigma(m=-infinity)(infinity)Sigma (r=-infinity)(infinity)alpha(mr )g(t-mT)exp(i2pirt/T'). The original Gabor transform proposed by D. Gabor (1946) is the special case of T=T'. The computation of the generalized Gabor transform with biorthogonal functions is discussed. The optimal biorthogonal functions are discussed. A relation between a window function and its optimal biorthogonal function is presented based on the Zak (1967) transform when T/T' is rational. The finite discrete generalized Gabor transform is also derived. Methods of computation for the biorthogonal function are discussed. The relation between a window function and its optimal biorthogonal function derived for the continuous variable generalized Gabor transform can be extended to the finite discrete case. Efficient algorithms for the optimal biorthogonal function and generalized Gabor transform for the finite discrete case are proposed. 相似文献
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Dual Gabor frames: theory and computational aspects 总被引:1,自引:0,他引:1
We consider a general method for constructing dual Gabor elements different from the canonical dual. Our approach is based on combining two Gabor frames such that the generated frame-type operator S/sub g,/spl gamma// is nonsingular. We provide necessary and sufficient conditions on the Gabor window functions g and /spl gamma/ such that S/sub g,/spl gamma// is nonsingular for rational oversampling, considering both the continuous-time and the discrete-time settings. In contrast to the frame operator, the operator S/sub g,/spl gamma// is, in general, not positive. Therefore, all results in Gabor analysis that are based on the positivity of the frame operator cannot be applied directly. The advantage of the proposed characterization is that the algebraic system for computing the Gabor dual elements preserves the high structure of usual Gabor frames, leading to computationally efficient algorithms. In particular, we consider examples in which both the condition number and the computational complexity in computing the proposed dual Gabor elements decrease in comparison to the canonical dual Gabor elements. 相似文献
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The undersampled discrete Gabor transform 总被引:1,自引:0,他引:1
Sigang Qiu 《Signal Processing, IEEE Transactions on》1998,46(5):1221-1228
Conventional studies on discrete Gabor transforms have generally been confined to the cases of critical sampling and oversampling in which the Gabor families span the whole signal space. In this paper, we investigate undersampled discrete Gabor transforms. For an undersampled Gabor triple (g,a,b), i.e. a·b>N, we show that the associated generalized dual Gabor window (GDGW) function is the same as the one associated with the oversampled (g,N/b,N/a), except for the constant factor (ab/N). Computations of undersampled Gabor transforms are made possible. By applying the methods (algorithms) developed in oversampled settings, the undersampled GDGW is determined. Then, we are able to obtain the best approximation of a signal x by linear combinations of vectors in the Gabor family 相似文献
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具有紧支采样函数的子波空间采样定理 总被引:1,自引:0,他引:1
从复制核Hilbert空间的观点出发,本文详细地讨论了子波空间采样定理,提出了子波空间推广的主尺度函数概念,证明了它是构造紧支子波空间采样函数的充要条件,从而得到具有紧支采样函数的子波空间采样定理。本文还详细地研究了推广的主正交尺度函数的性质,证明了紧支的推广主正交尺度函数所对应的子波函数仅有一阶消失矩,采样函数的紧支性和所对应的子波函数的光滑性是不可兼得的。 相似文献
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Balazs P. Feichtinger H. G. Hampejs M. Kracher G. 《Signal Processing, IEEE Transactions on》2006,54(12):4597-4610
The authors present an application of the general idea of preconditioning in the context of Gabor frames. While most (iterative) algorithms aim at a more or less costly exact numerical calculation of the inverse Gabor frame matrix, we propose here the use of "cheap methods" to find an approximation for it, based on (double) preconditioning. We thereby obtain good approximations of the true dual Gabor atom at low computational costs. Since the Gabor frame matrix commutes with certain time-frequency shifts, it is natural to make use of diagonal and circulant preconditioners sharing this property. Part of the efficiency of the proposed scheme results from the fact that all the matrices involved share a well-known block matrix structure. At least, for the smooth Gabor atoms typically used, the combination of these two preconditioners leads consistently to good results. These claims are supported by numerical experiments in this paper. For numerical evaluations we introduce two new matrix norms, which can be calculated efficiently by exploiting the structure of the frame matrix 相似文献
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kei F. Iacopi O. Richard J. Waeterloos S. Rozeveld E. Beach B. Mebarki T. Mandrekar S. Guggilla K. Maex 《Microelectronic Engineering》2003,70(2-4):352-357
Barrier integrity of Ta-films deposited using the enhanced coverage by re-sputtering (EnCoRe1) barrier was investigated on untreated surfaces of blanket porous SiLK, 2 semiconductor dielectric (developmental version 7, hereinafter v7). Barrier integrity of a bi-layer EnCoRe Ta(N)/Ta film was studied on single damascene lines using v7 and porous SiLK semiconductor dielectric (developmental version 9, hereinafter v9). On blanket wafers more than 30 nm barrier thickness is necessary to achieve complete pore sealing. Analysis of the sheet resistance showed that when tantalum is deposited, a low resistivity -phase is nucleated on the low-k surface. When deposited onto single damascene structures, EnCoRe Ta(N)/Ta is successful in providing a continuous metallic barrier layer over v7 and v9 semiconductor dielectric lines. 相似文献
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Pladdy C. zenOzen S. Nerayanuru S. M. Zoltowski M. Fimoff M. 《Vehicular Technology, IEEE Transactions on》2006,55(6):1812-1823
A semiblind iterative algorithm to construct the best linear unbiased estimate (BLUE) of the channel impulse response (CIR) vector h for communication systems that utilize a periodically transmitted training sequence within a continuous stream of information symbols is devised. The BLUE CIR estimate for the general linear model y=Ah+w, where w is the correlated noise, is given by the Gauss-Markoff theorem. The covariance matrix of the correlated noise, which is denoted by C(h), is a function of the channel that is to be identified. Consequently, an iteration is used to give successive approximations h(k),k=0,1,2,... to hBLUE, where h(0) is an initial approximation given by the correlation processing, which exists at the receiver for the purpose of frame synchronization. A function F(h) for which hBLUE is a fixed point is defined. Conditions under which hBLUE is the unique fixed point and for which the iteration proposed in the algorithm converges to the unique fixed point hBLUE are given. The proofs of these results follow broadly along the lines of Banach fixed-point theorems 相似文献
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We consider three different versions of the Zak (1967) transform (ZT) for discrete-time signals, namely, the discrete-time ZT, the polyphase transform, and a cyclic discrete ZT. In particular, we show that the extension of the discrete-time ZT to the complex z-plane results in the polyphase transform, an important and well-known concept in multirate signal processing and filter bank theory. We discuss fundamental properties, relations, and transform pairs of the three discrete ZT versions, and we summarize applications of these transforms. In particular, the discrete-time ZT and the cyclic discrete ZT are important for discrete-time Gabor (1946) expansion (Weyl-Heisenberg frame) theory since they diagonalize the Weyl-Heisenberg frame operator for critical sampling and integer oversampling. The polyphase representation plays a fundamental role in the theory of filter banks, especially DFT filter banks. Simulation results are presented to demonstrate the application of the discrete ZT to the efficient calculation of dual Gabor windows, tight Gabor windows, and frame bounds 相似文献
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In this paper, a biorthogonal-like sequences (BLS) theory and its application to the generalized Gabor expansions (equivalently, the generalized short-time Fourier transform/filterbank summation) are presented. A pair of BLS's are defined to be two sequences satisfying a biorthogonal-like condition (BLC), which is a moment equation and equivalent to a linear difference equation. We show that two collections in a Hilbert space generated by a pair of BLS's in the joint time-frequency domain are complete, either can be used as an analysis filter, and the other can be used as a synthesis filter for a generalized Gabor expansion of discrete-time signals. A sufficient and necessary condition on the existence of BLS's based on the moment equation is presented, which is simpler to use than frame theory. Given a filter generating a frame, its BLS's also generate frames. The dual frame is one of them. Given a FIR analysis/synthesis filter, there is a FIR synthesis/analysis filter if BLS's exist. The algorithm to compute FIR analysis and synthesis filters based on the linear difference equation is presented in this paper, which is simpler than frame operator 相似文献
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Kobayashi K. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》1997,43(3):816-826
A function h(w) is said to be useful for the coding theorem if the coding theorem remains to be true when the lengths |w| of codewords w in it are replaced with h(w). For a codeword w=a0a1...am-1 of length m and an infinite sequence Q=(q0, q1, q2, ...) of real numbers such that 0
n⩽½, let |w|Q denote the value Σn=0m-1 (if an =0 then -log2qn, else -log2(1-q n)), that is, -log2, (the probability that flippings of coins generate x) assuming that the (i+1)th coin generates a tail (or 0) with probability qi. It is known that if 0n→∞ qn then |w|Q is useful for the coding theorem and if limn→∞ q n/(1/(2n))=0 then |w|Q is not useful. We introduce several variations of the coding theorem and show sufficient conditions for h(w) not to be useful for these variations. The usefulness is also defined for the expressions that define the Kolmogorov complexity and the universal distribution. We consider the relation among the usefulness for the coding theorem, that for the Kolmogorov complexity, and that for the universal distribution 相似文献
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In this paper we introduce a class of Runge-Kutta multiresolution time-domain (RK-MRTD) methods for problems of electromagnetic wave propagation that can attain an arbitrarily high order of convergence in both space and time. The methods capitalize on the high-order nature of spatial multiresolution approximations by incorporating time integrators with convergence properties that are commensurate with these. More precisely, the classical MRTD approach is adapted here to incorporate mth-order m-stage low-storage Runge-Kutta methods for the time integration. As we show, if compactly supported wavelets of order N are used (e.g., the Daubechies D/sub N/ functions) and m=N, then the RK-MRTD methods deliver solutions that converge with this overall order; a variety of examples illustrate these properties. Moreover, we further show that the resulting algorithms are well suited to parallel implementations, as we present results that demonstrate their near-optimal scaling. 相似文献
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离散拟正交GaBor展开 总被引:2,自引:0,他引:2
利用一般条件的离散Zak变换及连续Gobor展开和离散Gabor展开间的关系。本文首次提出了在整数倍过抽样条件下,由Weyl-Heisenberg紧框架构造离散GABOR展开的方法。 相似文献
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Zhang Jiankang Bao Zheng 《Electronics letters》1998,34(5):451-452
The authors construct a three-band compactly supported orthogonal scaling function with an integer-shifted sampling property. Waiter's sampling theorem for wavelet subspaces corresponding to this scaling function has a compactly supported interplant. Therefore, the signals in multiresolution spaces can be reconstructed quickly and accurately without any truncation errors 相似文献
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If Γp is a p-ary code of length n, and a and b are two codewords, then c is called a descendant of a and b if ci ∈{ai, bi} for i=1,…,n. We are interested in codes Γp with the property that for any two codewords a and b their only descendant codewords are a and b themselves. This way a coalition of two users who are given codewords a and b cannot frame a third user who is given the codeword c. Intersecting codes over primary field GF(p) with the above mentioned property are found 相似文献
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This paper presents a novel area-efficient two's complement high radix divider without affecting the high speed of the radix-2k structure. In the proposed approach, only the odd values (rather than all the 2k values) of the quotient digit set are used to generate the multiples of divisor. Moreover, the set of (N+k+1)-bit additions are replaced with a set of few most significant bits (k+2 bits) additions followed by two (N+3)-bit additions only. The new radix-2k structure has been evaluated for different values of k. It is shown that the silicon area required by the new design could be as low as 15% of that of the conventional two's complement radix-2k architecture for radix-64 (20% for radix-32) while the speed is nearly the same. Despite that the proposed algorithm is originally developed in order to improve the performance of the two's complement approach, it has also been compared with the redundant SRT algorithm. The area–time ratios of the new radix-16 and radix-32 dividers to that of the SRT divider are equal to 85% and 77%, respectively. 相似文献
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Maximum likelihood reconstruction for emission tomography 总被引:28,自引:0,他引:28
Previous models for emission tomography (ET) do not distinguish the physics of ET from that of transmission tomography. We give a more accurate general mathematical model for ET where an unknown emission density lambda = lambda(x, y, z) generates, and is to be reconstructed from, the number of counts n(*)(d) in each of D detector units d. Within the model, we give an algorithm for determining an estimate lambdainsertion mark of lambda which maximizes the probability p(n(*)|lambda) of observing the actual detector count data n(*) over all possible densities lambda. Let independent Poisson variables n(b) with unknown means lambda(b), b = 1, ..., B represent the number of unobserved emissions in each of B boxes (pixels) partitioning an object containing an emitter. Suppose each emission in box b is detected in detector unit d with probability p(b, d), d = 1, ..., D with p(b,d) a one-step transition matrix, assumed known. We observe the total number n(*) = n(*)(d) of emissions in each detector unit d and want to estimate the unknown lambda = lambda(b), b = 1, ..., B. For each lambda, the observed data n(*) has probability or likelihood p(n(*)|lambda). The EM algorithm of mathematical statistics starts with an initial estimate lambda(0) and gives the following simple iterative procedure for obtaining a new estimate lambdainsertion mark(new), from an old estimate lambdainsertion mark(old), to obtain lambdainsertion mark(k), k = 1, 2, ..., lambdainsertion mark(new)(b)= lambdainsertion mark(old)(b)Sum of (n(*)p(b,d) from d=1 to D/Sum of lambdainsertion mark()old(b('))p(b('),d) from b(')=1 to B), b=1,...B. 相似文献