Signal-adapted biorthogonal interpolating recursive wavelet

A novel type of signal-adapted biorthogonal interpolating recursive wavelet (SABIRW) with explicit structural parameter vectors is constructed. By optimising the parameter vectors, the scaling function and wavelet can be adaptively selected at every level to obtain a compact multiresolution representation of the signal     

Optimal biorthogonal wavelet bases for signal decomposition

The selection of scaling functions for optimal signal representation by general multidimensional biorthogonal wavelet bases is investigated. Criterion for optimality is the minimization of the mean-square approximation error at each level of the decomposition. Conditions are given under which the approximation error of the decomposition approaches zero as the level increases. Given arbitrary synthesis filters, the optimal corresponding analysis filters are determined. Globally optimal families of filters are also found, and suboptimal linear and nonlinear-phase filters for the realization of the optimal scaling functions are explicitly determined     

适宜图像编码的双正交小波基的选择

提出一种新的选择适合图橡编码应用的双正交小波基的方法。通过用几个已证实是与图像编码密切相关的小波基评价标准对小波进行全面评价，选出了一些适宜图像编码应用的双正交小波基，并作了编码模拟检验。     

双正交小波在运动车辆图像压缩上的应用研究

智能交通控制系统中,针对车辆图像信息的传输技术过于消耗网络带宽的现状,给出了一种基于双正交小波的运动车辆图像压缩的方法。通过将每帧图片进行小波变换,只传输小波变换后的系数,且此系数包含了图像的大部分信息,大大减少了图像数据的传输流量,提高了控制系统的效率。最后对文中方法进行MATLAB仿真测试,并且与基于DCT的JPEG图像压缩方法进行了比较。     

A new class of biorthogonal wavelet systems for image transformcoding

We construct general biorthogonal Coifman wavelet systems, a new class of compactly supported biorthogonal wavelet systems with vanishing moments equally distributed for a scaling function and wavelet pair. A time-domain design method is employed and closed-form expressions for the impulse responses and the frequency responses of the corresponding dual filters are derived. The resulting filter coefficients are all dyadic fractions, which is an attractive feature in the realization of multiplication-free discrete wavelet transform. Even-ordered systems in this family are symmetric, which correspond to linear-phase dual filters. In particular, three filterbanks (FBs) in this family are systematically verified to have competitive compression potential to the 9-7 tap biorthogonal wavelet FB by Cohen et al. (1992), which is currently the most widely used one in the field of wavelet transform coding. In addition, the proposed FB's have much smaller computational complexity in terms of floating-point operations required in transformation, and therefore indicate a better tradeoff between compression performance and computational complexity.     

Simplified biorthogonal discrete wavelet transform for VLSI architecture design

Biorthogonal discrete wavelet transform (BDWT) has gained general acceptance as an image processing tool. For example, the JPEG2000 standard is completely based on the BDWT. In BDWT, the scaling (low-pass) and wavelet (high-pass) filters are symmetric and linear phase. In this work we show that by using a specific sign modulator the BDWT filter bank can be realized by only two biorthogonal filters. The analysis and synthesis parts use the same scaling and wavelet filters, which simplifies especially VLSI designs of the biorthogonal DWT/IDWT transceiver units. Utilizing the symmetry of the scaling and the wavelet filters we introduce a fast convolution algorithm for implementation of the filter modules. In multiplexer–demultiplexer VLSI applications both functions can be constructed via two running BDWT filters and the sign modulator. This work was supported by the National Technology Agency of Finland (TEKES).     

Parametrization construction of biorthogonal wavelet filter banks for image coding

We construct popular biorthogonal wavelet filter banks (BWFBs) having the linear phase and arbitrary multiplicity of vanishing moments (VMs). A novel parametrization construction technique, which is based on the theory of Diophantine equation, is presented and explicit one-parameter expressions of the BWFBs are derived. Using the expressions, any one-parameter family of BWFBs with different VMs can be constructed, and ten families, i.e., 5/7, 6/6, 9/7, 6/10, 5/11, 10/6, 13/7, 6/14, 17/11, and 10/18 families, are constructed here. The free parameter can be used to optimize the resulting BWFBs with respect to other criteria. In particular, in each family, three specific BWFBs with attractive features are obtained by adjusting the free parameter: the first has optimum coding gain and rational coefficients; the second which also has rational coefficients is very close to a quadrature mirror filter (QMF) bank; and the third which has binary coefficients can realize a multiplication-free discrete wavelet transform. In addition, four BWFBs are systematically verified to exhibit performance competitive to several state-of-the-art BWFBs for image compression, and yet require lower computational costs. This work was supported by the National Natural Science Foundation of China under Grant 60021302     

航空图像压缩的双正交小波滤波器整数化设计

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。     

RAPID PROTOTYPING - Framework for FPGA-based discrete biorthogonal wavelet transforms implementation

The discrete wavelet transform has taken its place at the forefront of research for the development of signal and image processing applications. These wavelet-based approaches have outperformed existing strategies in many areas including telecommunication, numerical analysis and, most notably, image/video compression. The authors present an investigation into the design and implementation of 1-D and 2-D discrete biorthogonal wavelet transforms (DBWTs) using a field programmable gate array (FPGA)-based rapid prototyping environment. The proposed architectures for DBWTs are scalable, modular and have less area and time complexity when compared with existing structures. FPGA implementation results based on a Xilinx Virtex-2000E device have shown that the proposed system provides an efficient solution for the processing of DBWTs in real-time     

Technique for designing biorthogonal wavelet filters with anapplication to image compression

A technique for designing new symmetric biorthogonal wavelets from a given symmetric regular filter is presented. The main idea is to find a symmetric complementary filter of a given regular filter such that it has the least mean square (LMS) amplitude deviation from the ideal halfband lowpass filter. New biorthogonal wavelet filter pairs can be obtained via factoring the product of the complementary polynomial and the given binomial. By applying these new symmetric biorthogonal wavelet filters to the compression of some complicated images an improved result in reducing artefacts may be achieved     

基于9/7双正交小波的一种高效矢量量化算法

该文提出一种用于图像压缩的矢量量化算法,该算法用9/7双正交小波对图像进行分解,利用三个方向上各自小波系数之间的相关性,构造符合其特征的跨频带矢量,提高了图像的编码效率和重构质量,同时采用了新的矢量量化技术渐进构造聚类(PCC),实验结果证明,该算法在未熵编码的条件下,获得 PSNR32dB的重构图像,比特率高达 0.141 bpp.而且实现方法十分简单。     

Construction of parametric biorthogonal wavelet filter banks with two parameters for image coding

We had presented a simple technique, which is based on the theory of Diophantine equation, for parametrization of popular biorthogonal wavelet filter banks (BWFBs) having the linear phase and arbitrary multiplicity of vanishing moments (VMs), and constructed a type of parametric BWFBs with one free parameter [15]. Here we generalize this technique to the case of two parameters, and construct a type of parametric BWFBs with two free parameters. The closed-form parameter expressions of the BWFBs are derived, with which any two-parameter family of BWFBs having preassigned VMs can be constructed, and six families, i.e., 9/11, 10/10, 13/11, 10/14, 17/11, and 10/18 families, are considered here. Two parameters provide two degrees of freedom to optimize the resulting BWFBs with respect to other criteria. In particular, in each family, three specific rational-coefficient BWFBs with attractive features are obtained by adjusting the parameters: the first is not only very close to a quadrature mirror filter (QMF) bank, but has optimum coding gain; the second possesses characteristics that are close to the irrational BWFB with maximum VMs by Cohen et al.; and the last which has binary coefficients can realize a multiplication-free discrete wavelet transform. In addition, two BWFBs are systematically verified to exhibit performance competitive to several state-of-the-art BWFBs for image compression, and yet require lower computational costs. This work was supported by the Natural Science Foundation of Jiangsu province, China under Grant 07KJD520005.     

On the utilization of periodic wavelet expansions in the momentmethods

In this paper, a new wavelet approach that makes use of periodic wavelet expansions in the moment methods is presented. The unknown field or response is expanded in terms of the periodic wavelet functions. As a wavelet expansion method, the moment-method matrix is rendered sparsely populated after applying a threshold procedure. Moreover, this approach circumvents the difficulties in the application of the conventional wavelet expansions on the real line to finite interval problems. A numerical study shows that this approach gives better accuracy than the use of the conventional wavelet expansions on the whole real line     

A new family of spline-based biorthogonal wavelet transforms and their application to image compression

In this paper. we design a new family of biorthogonal wavelet transforms and describe their applications to still image compression. The wavelet transforms are constructed from various types of interpolatory and quasiinterpolatory splines. The transforms use finite impulse response and infinite impulse response filters that are implemented in a fast lifting mode.     

Efficient linear system solution in moment methods using wavelet expansions

An efficient strategy is proposed to solve linear systems encountered when method of moments (MoM) and wavelet expansions are used. It exploits a high-performance matrix bandwidth reduction algorithm so that it can be taken advantage of direct banded solvers, which have a more favorable computational complexity with respect to the typically used iterative sparse methods. Speedups of up to seven have been experienced with respect to standard iterative sparse solvers.     

Popular biorthogonal wavelet filters via a lifting scheme and its application in image compression

A technique using a lifting scheme is presented for constructing compactly supported wavelets whose coefficients are composed of free variables locating in an interval. An efficient approach-based wavelet for image compression is developed by selecting the coefficients of the 9-7 wavelet filter and associated lifting scheme. Furthermore, the rationalised coefficients wavelet filter that can be implemented with simple integer arithmetic is achieved and its characteristic is close to the well known original irrational coefficients 9-7 wavelet filters developed by A. Cohen et al. (Commun. Pure Appl. Maths., vol.45, no.1, p.485-560, 1992). To reduce the computational cost of image coding applications further, an acceleration technique is proposed for the lifting steps. Software and hardware simulations show that the new method has very low complexity, and simultaneously preserves the high quality of the compressed image.     

Analysis of electromagnetic scattering from conducting bodies ofrevolution using orthogonal wavelet expansions

The wavelet expansion method has been extended to study the electromagnetic scattering from conducting bodies of revolution. The magnetic field integral equation (MFIE) is solved by this approach. By expanding the induced surface currents in terms of Fourier series of uncoupled azimuthal cylindrical modes, a simplified MFIE is attained for each unknown mode current that varies along the curved profile of the scatterer. By applying the boundary element method (BEM), the curved profile is mapped into the definition domain of the orthogonal wavelets on the interval. The unknown mode currents are then expressed using multiscale wavelet expansions. The simplified MFIE is converted into a sparse, multilevel matrix equation by the Galerkin method. Numerical examples are provided to illustrate the merits of this wavelet approach     

On the use of wavelet expansions in the method of moments [EMscattering]

An approach which incorporates the theory of wavelet transforms in method-of-moments solutions for electromagnetic wave interaction problems is presented. The unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function, which is often referred to as the mother wavelet. The wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer. The approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths. Using a Galerkin method and subsequently applying a threshold procedure, the moment-method matrix is rendered sparsely populated. The structure of the matrix reveals the localized scale-fitting distribution long before the matrix equation is solved. The performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double-slot aperture     

On the use of spatio-temporal wavelet expansions for transient analysis of wire antennas and scatterers

To analyze a wire antenna excited by a time varying voltage source or a wire scatterer excitated by transient electromagnetic incident wave, the problem is formulated in terms of a time-domain integral equation for the induced current. To solve the integral equation, we reduce it to matrix equation via the method of moments using the known-to-be-stable implicit scheme. However, rather than directly constructing and solving the relatively large matrix equation, we propose an iterative procedure which allows us to gradually obtain a solution of refined accuracy both everywhere and simultaneously at any time instance. To render this procedure rapidly converging, we use a basis of spatio-temporal wavelet functions. This basis facilitates a good approximation of the induced current using far less basis functions than would be needed if other expansions, such as standard-pulse or Fourier basis functions were chosen. The use of this basis further enables the iterative procedure to increase the temporal and spatial resolutions where required without unnecessarily affecting their levels elsewhere.