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基于Canny准则,参照最佳边缘滤波器的设计要求,确定选择用于边缘检测的小波母函数的一般准则。并在此基础上构造出二次B样条小波,提出了基于小波变换的多尺度自适应阈值图像边缘检测的新方法。 相似文献
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航空图像压缩的双正交小波滤波器整数化设计 总被引:1,自引:1,他引:0
在航空图像压缩中,通常采用具有线性相位、正则性、消失矩和完全重构,及适于硬件实现、实时等特性的小波。根据小波滤波器设计,提出了一种基于图像压缩的构造整数双正交小波滤波器的设计方法。从选择小波基的原则为出发点,以CDF9-7小波基为参考,以压缩效果为准则来构造出更优的双正交整数小波基,并且采用航空图像为标准训练图像,以压缩比、峰值信噪比、压缩后保留能量百分比为参数,来寻找最优的小波基。试验结果证明,此方法可以实施非常简单的、无浮点乘法的运算,因而减少运算复杂性以及降低小波硬件实现的难度。 相似文献
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根据连续时间滤波器设计理论,提出了一种基于开关电流双线性积分器和IFLF结构的取样数据小波滤波器设计方法。利用麦克劳林级数逼近小波频域函数,采用开关电流双线性积分器作为基本单元设计出传递函数为频域逼近函数的IFLF结构小波滤波器。通过调节滤波器时钟频率获得任意尺度小波函数实现连续小波变换。实验结果表明了该方法设计小波滤波器具有电路结构简单,小波函数尺度易于调节,通带灵敏度低的特点。 相似文献
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本文论述了由双正交完全重建滤波器组构造高度正则的双正交小波基的充分条件和构造方法,系统地研究了双正交线性相位FIR完全重建滤波器组的解的结构和已知H0(z)构造完全重建滤波器组的方法,并且实现了用单一的传递函数A(z)构造线性相位FIR双正交完全重建滤波器组的设计方法。这种方法的突出优点是滤波器组分析、合成部分中的滤波器可以用数值优化的方法使两者同时逼近理想低通滤波器和理想高通滤波器,即具有良好的频率选择性,并且所有滤波器都具有线性相位的特点。该滤波器组具有良好的梯形实现结构。在具体的滤波器设计中提出了基于均方误差最小准则的特征滤波器的设计方法和基于误差最大值最小准则的Remez交换法。而且上述方法设计的滤波器组可以构造出具有高度正则性的光滑的双正交小波基。 相似文献
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目前,基于提升格式的自适应小波变换多采用先更新后预测的结构.本文在Roger Claypoole研究的基础上提出了适用于自适应小波变换的新的提升格式滤波器.在更新过程,利用被更新系数两边的系数及其自身的值进行预更新操作.实验证明该滤波器具有更好的能量集中特性. 相似文献
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该文提出了基于多项式插值的预滤波器设计方法, 这种方法从分析尺度函数出发设计预滤波器。信号均匀采样时, 预滤波器是时不变滤波器, 其系数是分析尺度函数各阶矩的线性组合。预滤波器的逼近阶取决于分析尺度函数的支撑集长度而不是正则阶。该设计方法有两个突出的优点:可以设计比传统预滤波器更高逼近阶的预滤波器,如综合尺度函数整数点的值构成的特殊预滤波器和由预尺度函数法产生的预滤波器等,可以很自然地推广到信号非均匀采样的情况, 相应的预滤波器是时变滤波器, 逼近阶依赖于分析尺度函数的支撑集长度和采样点的分布。数值结果表明, 利用基于多项式插值的小波变换预滤波器可以得到逼近效果更好的初始尺度系数。 相似文献
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Symmetric prefilters for multiwavelets 总被引:3,自引:0,他引:3
Hsung T.-C. Sun M.-C. Lun D.P.-K. Siu W.-C. 《Vision, Image and Signal Processing, IEE Proceedings -》2003,150(1):59-68
When applying discrete multiwavelets, prefiltering is necessary because the initial multiscaling coefficients cannot be trivially derived from the samples of scalar signals. There have been many studies on the design of prefilters, and one main approach is to use a superfunction. The idea is to construct a low-pass function from the multiscaling functions that inherits their approximation power for scalar signals. However, none of the existing prefilters give linear phase combined filters, which is important for many practical applications. The authors analyse the conditions on which the prefilters and the combined filters are symmetric. A method is proposed for the design of good multiwavelet prefilters that allow the superfunction to be symmetric, satisfying the Strang-Fix conditions and the resulting combined filters are linear phase. Design examples using DGHM and Chui-Lian multiwavelets are given. 相似文献
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Multiwavelet moments and projection prefilters 总被引:1,自引:0,他引:1
An efficient projection procedure is derived for use of orthogonal multiwavelets in the analysis of discrete data sequences. A family of simple prefilters corresponding to numerical quadrature evaluation of the projection integrals provides exact results for locally polynomial data. The full approximation order of the multiwavelet basis can thus always be enabled. For nonpolynomial signals, the prefilters provide approximations to the coefficients of the multiwavelet series whose convergence accelerates quickly with increase in sampling rate. Comparison is also made with previous time-invariant multiwavelet prefilters 相似文献
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Adaptive multiwavelet initialization 总被引:8,自引:0,他引:8
The multiwavelet concept uses a set of scaling functions and a set of wavelets to generate an orthogonal multichannel multiresolution pyramid decomposition for finite energy signals. The multiple scaling functions extract the lowpass information of the input data set, and the multiwavelets extract the bandpass information. When the lowpass filters associated with the scaling functions are cascaded, a multiresolution pyramid decomposition/reconstruction system is formed with each pyramid convolution operator having several inputs and several outputs. However, there is only one data set available to initialize this process. This paper addresses the question of how to best modify the data set using prefilters so that its decomposition contains the most useful information for the chosen application. The “best” prefilters are determined by the minimization of the energy of preselected decomposition components. The resulting decomposition is, therefore, signal adaptive, and under appropriate conditions, perfect reconstruction of the input data set can be achieved with a proper postfiltering. The detailed discussions in the paper are focussed on the two-wavelet and two-scaling function case; the general multiwavelet case is addressed at the end of the paper. A compression example is provided to demonstrate the performance of the optimally initialized multiwavelet method and to compare it with a single wavelet method and another multiwavelet initialization method proposed by other authors 相似文献
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Multiwavelet prefilters. II. Optimal orthogonal prefilters 总被引:3,自引:0,他引:3
Attakitmongcol K. Hardin D.P. Wilkes D.M. 《IEEE transactions on image processing》2001,10(10):1476-1487
For pt.I see IEEE Trans. Circuits Syst. II, vol.45, p.1106-12 (1998). Prefiltering a given discrete signal has been shown to be an essential and necessary step in applications using unbalanced multiwavelets. In this paper, we develop two methods to obtain optimal second-order approximation preserving prefilters for a given orthogonal multiwavelet basis. These procedures use the prefilter construction introduced in Hardin and Roach (1998). The first prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. The second one is achieved by minimizing the energy compaction ratio (ECR) of the wavelet coefficients for an experimentally determined average input spectrum. We use both methods to find prefilters for the cases of the DGHM and Chui-Lian (CL) multiwavelets. We then compare experimental results using these filters in an image compression scheme. Additionally, using the DGHM multiwavelet with the optimal prefilters from the first scheme, we find that quadratic input signals are annihilated by the high-pass portion of the filter bank at the first level of decomposition. 相似文献
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The application of multiwavelet filterbanks to image processing 总被引:30,自引:0,他引:30
Strela V. Heller P.N. Strang G. Topiwala P. Heil C. 《IEEE transactions on image processing》1999,8(4):548-563
Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting for discrete-time signal and image processing. Multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank. We describe two methods (repeated row and approximation/deapproximation) for obtaining such a vector input stream from a one-dimensional (1-D) signal. Algorithms for symmetric extension of signals at boundaries are then developed, and naturally integrated with approximation-based preprocessing. We describe an additional algorithm for multiwavelet processing of two-dimensional (2-D) signals, two rows at a time, and develop a new family of multiwavelets (the constrained pairs) that is well-suited to this approach. This suite of novel techniques is then applied to two basic signal processing problems, denoising via wavelet-shrinkage, and data compression. After developing the approach via model problems in one dimension, we apply multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform. 相似文献
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A new prefilter design for discrete multiwavelet transforms 总被引:8,自引:0,他引:8
Xiang-Gen Xia 《Signal Processing, IEEE Transactions on》1998,46(6):1558-1570
In conventional wavelet transforms, prefiltering is not necessary due to the lowpass property of a scaling function. This is no longer true for multiwavelet transforms. A few research papers on the design of prefilters have appeared, but the existing prefilters are usually not orthogonal, which often causes problems in coding. Moreover, the condition on the prefilters was imposed based on the first-step discrete multiwavelet decomposition. We propose a new prefilter design that combines the ideas of the conventional wavelet transforms and multiwavelet transforms. The prefilters are orthogonal but nonmaximally decimated. They are derived from a very natural calculation of multiwavelet transform coefficients. In this new prefilter design, multiple step discrete multiwavelet decomposition is taken into account. Our numerical examples (by taking care of the redundant prefiltering) indicate that the energy compaction ratio with the Geronimo-Hardin-Massopust (1994) 2 wavelet transform and our new prefiltering is better than the one with Daubechies D4 wavelet transform 相似文献
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Balanced multiwavelet bases based on symmetric FIR filters 总被引:9,自引:0,他引:9
This paper describes a basic difference between multiwavelets and scalar wavelets that explains, without using zero moment properties, why certain complications arise in the implementation of discrete multiwavelet transforms. Assuming we wish to avoid the use of prefilters in implementing the discrete multiwavelet transform, it is suggested that the behavior of the iterated filter bank associated with a multiwavelet basis of multiplicity r is more fully revealed by an expanded set of r2 scaling functions φi,j. This paper also introduces new K-balanced orthogonal multiwavelet bases based on symmetric FIR filters. The nonlinear design equations arising in this work are solved using the Grobner basis. The minimal-length K-balanced multiwavelet bases based on even-length symmetric FIR filters are better behaved than those based on odd-length symmetric FIR filters, as illustrated by special relations they satisfy and by examples constructed 相似文献
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Tai-Chiu Hsung Lun D.P.-K. Yu-Hing Shum Ho K.C. 《Signal Processing, IEEE Transactions on》2007,55(12):5619-5629
Prefilters are generally applied to the discrete multiwavelet transform (DMWT) for processing scalar signals. To fully utilize the benefit offered by DMWT, it is important to have the prefilter designed appropriately so as to preserve the important properties of multiwavelets. To this end, we have recently shown that it is possible to have the prefilter designed to be maximally decimated, yet preserve the linear phase and orthogonal properties as well as the approximation power of multiwavelets. However, such design requires the point of symmetry of each channel of the prefilter to match with the scaling functions of the target multiwavelet system. It can be very difficult to find a compatible filter bank structure; and in some cases, such filter structure simply does not exist, e.g., for multiwavelets of multiplicity 2. In this paper, we suggest a new DMWT structure in which the prefilter is combined with the first stage of DMWT. The advantage of the new structure is twofold. First, since the prefiltering stage is embedded into DMWT, the computational complexity can be greatly reduced. Experimental results show that an over 20% saving in arithmetic operations can be achieved comparing with the traditional DMWT realizations. Second, the new structure provides additional design freedom that allows the resulting prefilters to be maximally decimated, orthogonal and symmetric even for multiwavelets of low multiplicity. We evaluated the new DMWT structure in terms of computational complexity, energy compaction ratio as well as the compression performance when applying to a VQ based image coding system. Satisfactory results are obtained in all cases comparing with the traditional approaches. 相似文献
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We systematically investigate the factorization of causal finite impulse response (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental order-one factorization form is first proposed for general paraunitary systems. Then, we develop a new structure for the design and implementation of paraunitary system based on the decomposition of Hermitian unitary matrices. Within this framework, the linear-phase filterbank and pairwise mirror-image symmetry filterbank are revisited. Their structures are special cases of the proposed general structures. Compared with the existing structures, more efficient ones that only use approximately half the number of free parameters are derived. The proposed structures are complete and minimal. Although the factorization theory with or without constraints is discussed in the framework of M-channel filterbanks, the results can be applied to wavelets and multiwavelet systems and could serve as a general theory for paraunitary systems 相似文献
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Vector wavelet transforms for vector-valued fields can be implemented directly from multiwavelets; however, existing multiwavelets offer surprisingly poor performance for transforms in vector-valued signal-processing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion known as omnidirectional balancing is introduced to extend to vector transforms the balancing philosophy previously proposed for multiwavelet-based scalar-signal expansion. It is shown that the straightforward implementation of a vector wavelet transform, namely, the application of a scalar transform to each vector component independently, is a special case of an omnidirectionally balanced vector wavelet transform in which filter-coefficient matrices are constrained to be diagonal. Additionally, a family of symmetric-antisymmetric multiwavelets is designed according to the omnidirectional-balancing criterion. In empirical results for a vector-field compression system, it is observed that the performance of vector wavelet transforms derived from these omnidirectionally-balanced symmetric-antisymmetric multiwavelets is far superior to that of transforms implemented via other multiwavelets and can exceed that of diagonal transforms derived from popular scalar wavelets. 相似文献