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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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本文主要分析了初级视觉中神经节细胞的感受反应将其感受响应函数作为基本子波函数(子波母函数),由此得出一对应视觉生理特性的二维子波变换,并且分析了这一子波变换在图象多分辨率轮廓提取中的应用。 相似文献
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针对目前用于信号(函数)逼近的子波神经网络的收敛速度慢的问题,提出一种子波网络的初值设定方法,使子波网络的收敛速度大大提高,通过对线性多项式、指数、三角函数及某些分段函数的实验以及与不同网络的对比,表明此方法具有很强的普适性 相似文献
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本文给出了独立子波函数理论的推导过程;然后结合目前已有的知识,给出一种独立子波函数的获得方法。在文章结构安排上,首先给出了独立子波函数的理论推导过程,然后运用EMD分解将一个信号分解成几个相互正交的信号,再将得到的相互正交的信号进行独立成分分析(ICA),得出几个相互独立的信号,即独立子波函数。 相似文献
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提出了一种基于小波变换分层和独立子波函数的单路混合信号的盲源分离新方法。首先讨论了单路混合信号分离模型,以及如何利用WPT进行窄带分层和获取独立子波函数的技术;然后通过结合独立子波函数进入单路混合信号,使单路混合信号由一维向量转化成为多维向量,以实现其盲分离;最后通过心音信号的分离实验,验证了本方法的有效性和可行性。 相似文献
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本文主要探讨了初级视觉中神经元感受野的Gabor表达,以及它与子波变换的关系,并在已建的广义Gabor函数模型的基础上,试图从生理意义上构建一组Gabor子波的基函数,并借助神经网络方法将综用于图象分析和数据压缩。 相似文献
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本文提出了一种基于独立子波函数和小波分析的单路含噪混合信号的盲源分离新方法.首先分析了独立子波函数的组成原理,以及获得独立子波函数的方法;然后通过结合独立子波函数进入单路混合信号,使单路混合信号由一维向量转化成为多维向量;其次讨论了利用小波进行二次去噪和解决数据段顺序不确定性的问题,并且文中还给出了独立子波函数个数判定方法和相似相图;最后通过消除瞬态诱发耳声发射中伪迹的实验,验证了本方法的有效性和可行性. 相似文献
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一种改进的子波域语音增强方法 总被引:13,自引:0,他引:13
本文基于文献[3]中提出的子波域去噪技术,并针对语音信号的特点提出了一种改进的子波域语音增强方法。该方法采用软限幅函数对语音信号的子波变换系数作阈值处理以达到去噪的目的。同时,为了防止在抑制噪声的过程中对语音的清音段信息造成损失,首先对语音信号进行了清浊音判别,然后针对不同的判别结果对清音段语音和浊音段语音采用不同的阈值处理方法。仿真实验表明,该方法效果良好且简便易行,是一种有效的语音增强技术。 相似文献
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本文提出利用DOG 函数作为子波基函数模拟人眼视觉信息提取过程。同时对普遍认为的视觉系统中存在着多个离散频率通道的观点提出质疑,提出了一种基于子波变换理论,具有反馈环节的中心频率和频带宽度可调的视觉信息提取通道模型。讨论了这一模型的特点和潜在的应用前景 相似文献
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Guangwen Pan Toupikov M.V. Gilbert B.K. 《Antennas and Propagation, IEEE Transactions on》1999,47(7):1189-1200
Orthonormal wavelets have been successfully used as basis and testing functions for the integral equations and extremely sparse impedance matrices have been obtained. However, in many practical problems, the solution domain is confined in a bounded interval, while the wavelets are originally defined on the entire real line. To overcome this problem, periodic wavelets have been described in the literature. Nonetheless, the unknown functions must take on equal values at the endpoints of the bounded interval in order to apply periodic wavelets as the basis functions. We present the intervallic Coifman wavelets (coiflets) for the method of moments (MoM). The intervallic wavelets release the endpoints restrictions imposed on the periodic wavelets. The intervallic wavelets form an orthonormal basis and preserve the same multiresolution analysis (MRA) of other usual unbounded wavelets. The coiflets possesses a special property that their scaling functions have many vanishing moments. As a result, the zero entries of the matrices are identified directly, without using a truncation scheme with an artificially established threshold. Further, the majority of matrix elements are evaluated directly without performing numerical integration procedures such as Gaussian quadrature. For an n×n matrix, the number of actual numerical integrations is reduced from n2 to the order of 3n(2L-1), when the coiflets of order L is employed. The construction of intervallic wavelets is presented. Numerical examples of scattering problems are discussed and the relative error of this method is studied analytically 相似文献
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New families of Fourier eigenfunctions for steerable filtering 总被引:1,自引:0,他引:1
A new diadic family of eigenfunctions of the 2-D Fourier transform has been discovered. Specifically, new wavelets are derived by steering the elongated Hermite-Gauss filters with respect to rotations, thus obtaining a natural generalization of the Laguerre-Gauss harmonics. Interestingly, these functions are also proportional to their 2-D Fourier transform. Their analytical expression is provided in a compact and treatable form, by means of a new ad hoc matrix notation in which the cases of even and odd orders of the Hermite polynomials are unified. Moreover, these functions can be efficiently implemented by means of a recursive formula that is derived in this paper. The proposed filters are applied to the problem of gradient estimation to improve the theoretical Canny tradeoff of position accuracy versus noise rejection that occurs in edge detection. Experimental results show considerable improvements in using the new wavelets over both isotropic Gaussian derivatives and other elongated steerable filters more recently introduced. Finally, being the proposed wavelets a set of Fourier eigenfunctions, they can be of interest in other fields of science, such as optics and quantum mechanics. 相似文献
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Zhuoer Shi Wei G.W. Kouri D.J. Hoffman D.K. Zheng Bao 《IEEE transactions on image processing》2001,10(10):1488-1508
This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach combines the perceptually dependent visual group normalization (VGN) technique and a softer logic masking (SLM) method. These are utilized to rescale the wavelet coefficients, remove perceptual redundancy and obtain good visual performance for digital image processing. 相似文献
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基于Bubble小波的多尺度边缘提取 总被引:19,自引:0,他引:19
侧抑制是生物视觉信息处理中广泛存在的一种机制,Bubble函数很好刻画了侧抑制现象。本文利用Bubble函数构成小波,高斯函数作为平滑函数,用Mallat快速算法进行小波分解,分解的局部极大值就是多尺度边缘,理论和实验都表明,这种算法对于不同的尺度,有洋同的抑制噪声的能力和提取边缘细节的能力。当Bubble函数的尺度较大时,抑制噪声的能力增强,提取边缘细节的能力变差;当Bubble函数的尺度较小时 相似文献
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Wavelets with convolution-type orthogonality conditions 总被引:5,自引:0,他引:5
Wavelets with free parameters are constructed using a convolution-type orthogonality condition. First, finer and coarser scaling function spaces are introduced with the help of a two-scale relation for scaling functions. An inner product and a norm having convolution parameters are defined in the finer scaling function space, which becomes a Hilbert space as a result. The finer scaling function space can be decomposed into the coarser one and its orthogonal complement. A wavelet function is constructed as a mother function whose shifted functions form an orthonormal basis in the complement space. Such wavelet functions contain the Daubechies' compactly supported wavelets as a special case. In some restricted cases, several symmetric and almost compactly supported wavelets are constructed analytically by tuning free convolution parameters contained in the wavelet functions 相似文献
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《AEUE-International Journal of Electronics and Communications》2014,68(7):616-622
The Daubechies, coiflet and symlet wavelets, with properties of orthogonal wavelets are suitable for multicarrier transmission over band-limited channels. It has been shown that similar wavelets can be constructed by Lagrange approximation interpolation. In this work and using established wavelet design algorithms, it is shown that ideal filters can be approximated to construct new orthogonal wavelets. These new wavelets, in terms of BER, behave slightly better than the wavelets mentioned above, and much better than biorthogonal wavelets, in multipath channels with additive white Gaussian noise (AWGN). It is shown that the construction, which uses a simple simultaneous solution to obtain the wavelet filters from the ideal filters based on established wavelet design algorithms, is simple and can easily be reproduced. The Cramer–Rao lower bound is applied to access the BER performance of the proposed wavelet. 相似文献
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The asymmetry of Daubechies' (1988, 1992) scaling functions and wavelets can be diminished by minimizing a special second moment in time for the wavelet-generating discrete-time filter. The moment is involved in an uncertainty relation for discrete-time signals. Other measures of asymmetry are addressed as well, and corresponding results are compared 相似文献
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This paper develops an overcomplete discrete wavelet transform (DWT) based on rational dilation factors for discrete-time signals. The proposed overcomplete rational DWT is implemented using self-inverting FIR filter banks, is approximately shift-invariant, and can provide a dense sampling of the time-frequency plane. A straightforward algorithm is described for the construction of minimal-length perfect reconstruction filters with a specified number of vanishing moments; whereas, in the nonredundant rational case, no such algorithm is available. The algorithm is based on matrix spectral factorization. The analysis/synthesis functions (discrete-time wavelets) can be very smooth and can be designed to closely approximate the derivatives of the Gaussian function. 相似文献