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.

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.

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.

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.

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.

Implementation of Texture Based Image Retrieval Using M-band Wavelet Transform

Wavelet transform has attracted attention because it is a very useful tool for signal analyzing. As a fundamental characteristic of an image, texture traits play an important role in the human vision system for recognition and interpretation of images. The paper presents an approach to implement texture-based image retrieval using M-band wavelet transform. Firstly the traditional 2-band wavelet is extended to M-band wavelet transform. Then the wavelet moments are computed by M-band wavelet coefficients in the wavelet domain. The set of wavelet moments forms the feature vector related to the texture distribution of each wavelet images. The distances between the feature vectors describe the similarities of different images. The experimental result shows that the M-band wavelet moment features of the images are effective for image indexing. The retrieval method has lower computational complexity, yet it is capable of giving better retrieval performance for a given medical image database.

THEORY OF ORTHONORMAL M-BAND WAVELET PACKETS

In recent years, M-band orthonormal wavelet bases, due to their good characteristics, have attracted much attention. The ability of 2-band wavelet packets to decompose high frequency channels can be employed to improve the performance of wavelets for time-frequency localization, which makes more kinds of signals for analyzing by wavelets. Similar to the notations from the extension of 2-band wavelets to 2-band wavelet packets, the theoretic framework of M-band wavelet packets is developed, a generalization of the notations and properties of 2-band wavelet packets to that of M-band wavelet packets is made and the corresponding proofs are given.

ICI elimination of M-band wavelet multi-carrier modulation system

To solve the inter carrier interference （ICI） elimination problem of an M-band wavelet multi-carrier modulation system, this paper analyzes the principle of the ICI caused by the Doppler frequency shift and its mathematical expression based on the M-band wavelet multi-carrier modulation system model. Through the analysis of the mathematical expression and combining with the perfect reconstruction conditions of the filter banks, we propose the design conditions of an M-band filter to reduce and eliminate the ICI. The impulse response model of the filter design conditions and an iterative algorithm is also established. The simulation results show that the proposed ICI reduction and elimination methods can effectively improve the system performance.

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.

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.

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.

A NEW METHOD FOR SOLVING MSDE BASED ON WAVELET NEURAL NETWORKS

In this paper, a new method to solve multiscale difference equation(MSDE) with the M-band wavelet neural networks is proposed. It is shown that the method has many advantages over the existing methods and enlarges the range of the solvable equations.

Wavelet Adaptive Bitzerotree Coding for Video

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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.

n-d m-band Generalized Multiresolution Analysis and Its Applications

In this paper, we extend the generalized multiresolution analysis （GMRA） to higher dimensional spaces. The GMRA is generalized from each ladder space expanded by a different scaling function with positive integer dilation factor m ≥2. The n-d GMRA is discussed in orthogonal and bi-orthogonal cases. Then the optimal m-band wavelets are applied in processing the image datasets of the human body slices. The efficiency and superiority of the algorithm can be seen from the processing results.

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.