FREQUENCY OPTIMIZATION APPROACH FOR DESIGNING M-BAND BIORTHOGONAL SYMMETRIC WAVELETS

In this paper,a new method is presented for designing M-band biorthogonal symmetric wavelets.The design problem of biorthogonal linear-phase scaling filters and wavelet filters as a quadratic programming problem with the linear constraints is formulated.The closed-form solution is given and a design example is presented.

P wave onset time picking with the B-spline biorthogonal wavelet

The seismic wave consists of many seismic phases, which contain rich geophysical information from the hypocenter, medium of seismic wave passing through and so on. It is very important to detect and pick these seismic phases for understanding the mechanism of earthquake, the Earth structure and property of seismic waves. In order to reduce or avoid the loss resulted from the earthquake, one of the important goals of seismic event detecting is to obtain its related information before and after it occurs. Because of the particularity of P wave and S wave the seismic event detecting focuses on distinguishing P and S waves and picking their onset time, it has been becoming one of the research hotspots for many geophysicists to pick the P and S wave arrival accurately and effectively.

On the Zeros of Daubechies Orthogonal and Biorthogonal Wavelets

In the last decade, Daubechies’ wavelets have been successfully used in many signal processing paradigms. The construction of these wavelets via two channel perfect reconstruction filter bank requires the identification of necessary conditions that the coefficients of the filters and the roots of binomial polynomials associated with them should exhibit. In this paper, orthogonal and Biorthogonal Daubechies families of wavelets are considered and their filters are derived. In particular, the Biorthogonal wavelets Bior3.5, Bior3.9 and Bior6.8 are examined and the zeros distribution of their polynomials associated filters are located. We also examine the locations of these zeros of the filters associated with the two orthogonal wavelets db6 and db8.

The Biorthogonality of Multiple Vector-valued Bivariate Wavelet Packets

The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.

A Wavelet Multigrid Method Using Symmetric Biorthogonal Wavelets

In [1], the author introduced a wavelet multigrid method that used the wavelet transform to define the coarse grid, interpolation, and restriction operators for the multigrid method. In this paper, we modify the method by using symmetric biorthogonal wavelet transforms to define the requisite operators. Numerical examples are presented to demonstrate the effectiveness of the modified wavelet multigrid method for diffusion problems with highly oscillatory coefficients, as well as for advection-diffusion equations in which the advection is moderately dominant.

拟半双正交分数阶多小波框架的刻画

本文在半正交分数阶多小波框架的基础上,运用多分辨分析,泛函分析,矩阵理论研究L~2(R)上多元小波框架的特征,将半正交分数阶多小波框架推广到拟半双正交分数阶多小波框架,给出了拟半双正交分数阶多小波框架的概念,得到了严格拟半双正交分数阶多小波框架的等价条件,证明了广义多分辨分析分数阶规范对偶多小波框架与拟半双正交分数阶规范对偶多小波框架满足等价条件.

Seismic data compression based on integer wavelet transform

Due to the particularity of the seismic data, they must be treated by lossless compression algorithm in some cases. In the paper, based on the integer wavelet transform, the lossless compression algorithm is studied. Comparing with the traditional algorithm, it can better improve the compression rate. CDF (2, n) biorthogonal wavelet family can lead to better compression ratio than other CDF family, SWE and CRF, which is owe to its capability in can- celing data redundancies and focusing data characteristics. CDF (2, n) family is suitable as the wavelet function of the lossless compression seismic data.

Wavelet Adaptive Bitzerotree Coding for Video

ＷａｖｅｌｅｔＡｄａｐｔｉｖｅＢｉｔｚｅｒｏｔｒｅｅＣｏｄｉｎｇｆｏｒＶｉｄｅｏＨｅｎｇＷｅｉ（衡伟）ＦｕＹｕｑｉｎｇ（富煜清）ＷｅｉＺｈｉｈｕｉ（韦志辉）ＣｈｅｎｇＳｈｉｘｉｎｇ（程时昕）（ＤｅｐａｒｔｍｅｎｔｏｆＲａｄｉｏＥｎｇｉｎｅｅｒｉｎｇ，...

Singularity Detecting with the SecondGeneration Wavelet

Adopting the lifting scheme, introduced by Sweldens, a new wavelet is constructed. It overcomes the shortcoming of the classical wavelets that has no flexibility in the number of vanishing moment. Two examples are given to prove the second-generation wavelets's potentialities in the singularity detection of signal: a wavelet with vanishing moment and symmetry can be constructed according to the problem. Key words biorthogonal wavelet - lifting scheme - secondgeneration wavelets - singularity CLC number O 174.2 Foundation item: Supported by the National Natural Science Foundation of China (19602014)Biography: XU Bing-lian (1977-), female, Master candidate, research direction: the wavelets application.

The Boundary Processing of Wavelet Based Image Compression

When an image, which is decomposed by bi-orthogonal wavelet bases, is reconstructed, some information will be lost at the four edges of the image. At the same time, artificial discontinuities will be introduced. We use a method called symmetric extension to solve the problem. We only consider the case of the two-band filter banks, and the results can be applied to M-band filter banks. There are only two types of symmetric extension in analysis phrase, namely the whole-sample symmetry (WS), the half-sample symmetry (HS), while there are four types of symmetric extension in synthesis phrase, namely the WS, HS, the whole-sample anti-symmetry (WA), and the half-sample anti-symmetry (HA) respectively. We can select the exact type according to the image length and the filter length, and we will show how to do these. The image can be perfectly reconstructed without any edge effects in this way. Finally, simulation results are reported. Key words edge effect - image compression - wavelet - biorthogonal bases - symmetric extension CLC number TP 37 Foundation item: Supported by the National 863 Project (20021111901010)Biography: Yu Sheng-sheng (1944-), male, Professor, research direction: multimedia information processing, SAN.

Methods of Constructing Optimal Wavelet Filters Based on Genetic Algorithm

In this paper, algorithms of constructing wavelet filters based on genetic algorithm are studied with emphasis on how to construct the optimal wavelet filters used to compress a given image, due to efficient coding of the chromosome and the fitness function, and due to the global optimization algorithm, this method turns out to be perfect for the compression of the images.

Performance Evaluation of Wavelet Based on Human Visual System

We have constructed a compactly supported biorthogonal wavelet that approximates the modulation transfer function (MTF) of human visual system in the frequency domain. In this paper, we evaluate performance of the constructed wavelet, and compare it with the widely used Daubechies 9 7, Daubechies 9 3 and GBCW 9 7 wavelets. The result shows that coding performance of the constructed wavelet is better than Daubechies 9 3, and is competitive with Daubechies 9 7 and GBCW 9 7 wavelets. Like Daubechies 9 3 wavelet, the filter coefficients of the constructed wavelet are all dyadic fractions, and the tap is less than Daubechies 9 7 and GBCW 9 7. It has an attractive feature in the realization of discrete wavelet transform.

Tracking of Non-Rigid Object in Complex Wavelet Domain

In this paper we have proposed an object tracking method using Dual Tree Complex Wavelet Transform (DTCxWT). The proposed method is capable of tracking the moving object in video sequences. The object is assumed to be deform-able under limit i.e. it may change its shape from one frame to another. The basic idea in the proposed method is to decompose the image into two components: a two dimensional motion and a two dimensional shape change. The motion component is factored out while the shape is explicitly represented by storing a sequence of two dimensional models. Each model corresponds to each image frame. The proposed method performs well when the change in the shape in the consecutive frames is small however the 2-D motion in consecutive frames may be large. The proposed algorithm is capable of handling the partial as well as full occlusion of the object.

基于双正交样条小波的输油管道焊接缺陷漏磁信号识别技术

针对输油管道焊接缺陷漏磁信号量大,无法精准检测漏磁信号磁场强度,影响识别效果的问题,提出基于双正交样条小波的输油管道焊接缺陷漏磁信号识别技术。应用双正交样条小波技术分解信号,采用稀疏矩阵求解器分解磁感应强度。计算连续小波变换系数和缺陷内漏磁场场磁导率,明确不同介质磁感应强度和场磁导率关系,识别凹、凸缺陷漏磁信号。实验结果表明,该技术凹形缺陷磁场强度检测结果只在峰值处出现了与实际数据最大为50 A/m的偏差,凸形缺陷磁场强度检测结果与实验数据一致。

Biorthogonal multiple wavelets generated by vector refinement equation

Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis.In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form （?）（x）=（?）a（α）（?）（Mx-α）,x∈Rs, where the vector of functions（?）=（（?）1,...,（?）r）T is in（L2（Rs））r,a=:（a（α））α∈Zsis a finitely supported sequence of r×r matrices called the refinement mask,and M is an s×s integer matrix such that limn→∞M-n=0.Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.

General Solutions of Matrix Extension Associated with Multiple Channel Biorthogonal Wavelet Filters

This paper is concerned with seeking the general solutions of matrix equation M（ξ）M＊ （ξ） = Is for the construction of multiple channel biorthogonal wavelets, provided that some special solution of its is known.

基于差分双正交小波熵的电力电缆故障定位方法

在电力电缆故障定位的过程中,受原始电力电缆运行状态信号特征的影响,导致定位结果误差较大,为此提出基于差分双正交小波熵的电力电缆故障定位方法研究。对原始电力电缆运行状态信号的多分辨率小波分解处理后,采用了差分预处理方式提取差分双正交小波熵。将电力信号的差分双正交小波熵作为故障信号的定位基准参数,确定具体的故障位置。在测试结果中,故障的定位结果不受故障类型和故障距离的影响,且对应的误差基本稳定在2.5%以内。

Local Analysis, Cardinality, and Split Trick of Quasi-biorthogonal Frame Wavelets

The notion of quasi-biorthogonal frame wavelets is a generalization of the notion of orthog- onal wavelets. A quasi-biorthogonal frame wavelet with the cardinality r consists of r pairs of functions. In this paper we first analyze the local property of the quasi-biorthogonal frame wavelet and show that its each pair of functions generates reconstruction formulas of the corresponding subspaces. Next we show that the lower bound of its cardinalities depends on a pair of dual frame multiresolution analyses deriving it. Finally, we present a split trick and show that any quasi-biorthogonal frame wavelet can be split into a new quasi-biorthogonal frame wavelet with an arbitrarily large cardinality. For generality, we work in the setting of matrix dilations.

数字水印中的双正交小波基

研究了DWT域水印算法中的双正交小波基。首先提出了双正交小波的分析与综合小波的选择标准 ,并据此标准得到一些结论。然后通过对著名且广泛应用的Daubechies双正交滤波器 9 7、 7 9、 5 3、 3 5、 7 5、 5 7、9 3和 3 9的稳健性能进行比较 。

不同小波基下滤波性能之比较

不同的小波基有各自的特点和优点。对三种典型的具有紧支撑的小波 ,即Haar小波、正交小波[1] 、双正交小波[2 ] 在滤波中的应用进行了研究 ,对其滤波效果进行了对比并分析了其原因。指出了Haar小波具有最高的时间分辨率 ,能够对信号的瞬态特征进行很好的识别 ;而正交和双正交小波具有二阶的消失矩 ,对信号的逼近精度高。但正交小波缺乏对称 (反对称 )性 ,有可能造成较多的失真。若能做到对信号的不同特征自适应地采用不同的小波基进行分析 ,则可使滤波效果达到最佳。