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The lifting scheme of 4-channel orthogonal wavelet transforms

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Progress in Natural Science:Materials International 2006年第1期16卷 100-104页

作者： PENG Lizhong and CHU Xiaoyong (LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China) LMAM School of Mathematical Sciences Peking University Beijing 100871 China

The 4-channel smooth wavelets with linear phase and orthogonality are designed from the 2-channel orthogonal wavelets with high transfer vanishing moments. Reversely, for simple lifting scheme of such 4-channel orthogonal wavelet transforms, a new 2-channel orthogonal wavelet associated with this 4-channel wavelet is constructed. The new 2-channel wavelet has at least the same number of vanishing moments as the associated 4-channel one. Finally, by combining the two such 2-channel wavelet systems, the lifting scheme of 4-channel orthogonal wavelet transform, which has simple structure and is easy to apply, is presented.

关键词： lifting scheme 4-channel orthogonal wavelet 2-channel orthogonal wavelet vanishing moment transfer vanishing moment linear phase.

lifting scheme Based SPIHT Still Image Coding

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Journal of Beijing Institute of Technology 2003年第S1期12卷 70-74页

作者：沈利军赵保军何佩琨 Department of Electronic Engineering School of Information Science and TechnologyBeijing Institute of TechnologyBeijing 100081China

In order to eliminate float-point operations for fast wavelet transform, an integer D9/7 biorthogonal reversible wavelet transform was accomplished by lifting scheme. The lifting scheme based wavelet transform can be finished by addition and shift simply. It improved the quality of reconstructive image and greatly reduced the computational complexity due to integer operation. It is suitable for real-time image coding on hardware such as DSP. The simulation results show that the lifting scheme based SPIHT is prior to traditional wavelet based SPHIT in quality and complexity.

关键词： SPIHT lifting scheme wavelet image coding

The lifting scheme Based on the Second Generation Wavelets

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Wuhan University Journal of Natural Sciences 2006年第3期11卷 503-506页

作者： FENG Hui GUO Lanying XIAO Jinsheng School of Mathematics and Statistics Wuhan University Wuhan 430072 Hubei China School of Electronic Information Wuhan UniversityWuhan 430072 Hubei China

The lifting scheme is a custom design construclion of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform,which provides a wider range of application and efficiently reduces the computing time with its particular frame. This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets. Because of isolating the degrees of freedom remaining the biorthogonality relations, we can fully control over the lifting operators to design the wavelet for a particular application, such as increasing the number of the vanishing moments.

关键词： lifting scheme the second generation wavelets vanishing moments

An Improved Algorithm for Image Edge Detection Based on lifting scheme

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Journal of Electronic Science and Technology of China 2005年第2期3卷 113-115,133页

作者：张红英吴斌彭启琮 School of Communication and Information Engineering University of Electronic Science and Technology of China Chengdu 610054 China School of Information and Control Engineering Southwest University of Science and Technology Mianyang Sichuan 621002 China

Wavelet transform is an ideal way for edge detection because of its multi-scale property, localization both in time and frequency domain, sensitivity to the abrupt change of signals, and so on. An improved algorithm for image edge detection based on lifting scheme is proposed in this paper. The simulation results show that our improved method can better reflect edge information of images.

关键词： lifting scheme edge detection image processing second generation wavelet

Construct the Biorthogonal Balanced Multiwavelets by lifting scheme

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Construct the Biorthogonal Balanced Multiwavelets by Lifting...

2011 IEEE International Conference on Computer Science and Automation Engineering(CSAE 2011)

作者： Yu Shen 12 Xieping Gao 2 Fang Pu 1 Linlang Liu 1 Qiying Cao 11 Informationization Office Donghua University Shanghai China 2 College of Information and Engineering Xiangtan University Xiangtan China

After the introduction of the lifting scheme and the Balanced Multiwavelets, we put forward the equivalent condition between approximation and balance, and using the condition to construct the biorthogonal balanced multiwavelets by lifting scheme. This method blend the balanced condition in the lifting scheme, and the multiwavelets constructed by this method has balanced property directly. In addition, experimental results of applying these multiwavelets to image compression are presented.

关键词： Balanced Multiwavelets lifting scheme

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利用提升格式构造稳定的对偶小波

高等学校计算数学学报 2001年第4期23卷 330-339页

作者：周先波中山大学岭南学院经济系广州510275

By using lifting scheme and starting with B-spline filters and Daubechies-counter-example filter respectively, we obtain biorthogonal filters which generate stable dual wavelets.

关键词： lifting scheme wavelet Riesz basis B-spline filters Daubechies-counter-example filter.

Low complexity reconfigurable architecture for the 5/3 and 9/7 discrete wavelet transform

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Journal of Systems Engineering and Electronics 2006年第2期17卷 303-308页

作者： Xiong Cheng yi Tian Jinwen Liu Jian Coll. of Electronic Information Engineering South Center Univ. for Nationalities Wuhan 430074 P.R. China Inst. of Pattern Recognition & Artificial Intelligence Key Lab. of Education Ministry for Image Processing and Intelligent Control Huazhong Univ. of Science & Technology Wuhan 430074 P.R. China

Efficient reconfigurable VLSI architecture for 1-D 5/3 and 9/7 wavelet transforms adopted in JPEG2000 proposal, based on lifting scheme is proposed. The embedded decimation technique based on fold and time multiplexing, as well as embedded boundary data extension technique, is adopted to optimize the design of the architecture. These reduce significantly the required numbers of the multipliers, adders and registers, as well as the amount of accessing external memory, and lead to decrease efficiently the hardware cost and power consumption of the design. The architecture is designed to generate an output per clock cycle, and the detailed component and the approximation of the input signal are available alternately. Experimental simulation and comparison results are presented, which demonstrate that the proposed architecture has lower hardware complexity, thus it is adapted for embedded applications. The presented architecture is simple, regular and scalable, and well suited for VLSI implementation.

关键词： VLSI discrete wavelet transform lifting scheme embedded decimation reeonfigurable.

A Study on Wavelet Data Compression of a Real-Time Monitoring System for Large Hydraulic Machines

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Journal of Computer Science & Technology 2001年第3期16卷 293-296页

作者：王海郑莉媛 Department of Power Engineering Huazhong University of Science & Technology Wahan P.R. China

The general concept of data compression consists in removing the redundancy existing in data to find a more compact representation. This paper is concerned with a new method of compression using the second generation wavelets based on the lifting scheme, which is a simple but powerful wavelet construction method. It has been proved by its successful application to a real-time monitoring system of large hydraulic machines that it is a promising compression method.

关键词： data compression lifting scheme second generation wavelets

Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval

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Applied Mathematics and Mechanics(English Edition) 2009年第10期30卷 1325-1334页

作者：向家伟陈雪峰李锡夔 Faculty of Mechanical and Electrical Engineering Guilin University of Electronic Technology State Key Laboratory for Manufacturing Systems Engineering Xi'an Jiaotong University State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology

A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.

关键词： Poisson equation Hermite cubic spline wavelet lifting scheme waveletbased finite element method