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cascade algorithm and multiresolution analysis on the Heisenberg group

Progress in Natural Science:Materials International 2005年第7期15卷 602-608页

作者： LIU Heping, LIU Yu, 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

In this paper we investigate the relationship between the convergence of cascade algorithm and orthogonal (or biorthogo-nal) multiresolution analysis on the Heisenberg group. It is proved that the (strong) convergence of cascade algorithm together with the perfect reconstruction condition induces an orthogonal multiresolution analysis and vice versa . Similar results are also proved for biorthogo-nal multiresolution analysis.

关键词： Heisenberg group cascade algorithm multiresolution analysis refinable functions.

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A NOTE ON VECTOR cascade algorithm

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Journal of Computational Mathematics 2002年第4期20卷 363-372页

作者： Qiu-hui Chen Jin-zhao Liu Wen-sheng Zhang Department of Scientific Computing and Computer Applications Zhongshan UniversityGuangzhou510275China Department of Geophysics Peking UniversityBeijing 100871China ICMSEC Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijing 100080China

The focus of this paper is on the relationship between accuracy of multivariate refinable vector and vector cascade algorithm. We show that, if the vector cascade algorithm (1.5) with isotropic dilation converges to a... 详细信息

关键词： cascade algorithm accuracy symbol refinable vector

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Longitudinal tear detection of conveyor belt under uneven light based on Haar-AdaBoost and cascade algorithm

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MEASUREMENT 2021年 168卷 108341-108341页

作者： Wang, Gongxian Zhang, Libin Sun, Hui Zhu, Chao Wuhan Univ Technol Sch Logist Engn Wuhan 430063 Hubei Peoples R China

As the light of the belt conveyor changes drastically and unevenly, it will cause the longitudinal tear detection rate of the traditional methods drop sharply. To improve the situation, a novel method, which replaces the traditional geometric features with the Haar features, is proposed. First, the Haar feature was employed to train weak classifiers. Then, the AdaBoost algorithm is utilized to upgrade the weak classifiers to strong classifiers. Finally, the cascade algorithm is introduced to combine strong classifiers in series into a cascade classifier that can reduce the training and processing time. The experiment following the above proposed method has shown that the recall, accuracy, and precision of tear detection under uneven light almost approaches the level under the uniform light (less than 3% difference), which indicates that our method is more accurate and robust than the existing methods in real-time belt tear detection.

关键词： cascade algorithm Conveyor belt Haar-AdaBoost algorithm Longitudinal tear detection Real time

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Information collection system for fall detection of stroke patients under cascade algorithm in the context of multi-modal information fusion and e-health

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EXPERT SYSTEMS 2023年第4期40卷 e12809-e12809页

作者： Lv, Xiao Ma, Dingying Zhou, Jinsheng Zhang, Lili Li, Xinke Ningbo Ninth Hosp Dept Phys Med & Rehabil 68 Xiangbei Rd Ningbo 315020 Zhejiang Peoples R China Ningbo First Hosp Dept Phys Med & Rehabil Ningbo Peoples R China

To effectively detect stroke patients after falling under e-health, the fall situation of patients is graded, and warnings are given to improve the survival probability of stroke patients after falling. First, the fall model of stroke patients is analysed. According to the model, multi-modal information fusion fall detection technology is proposed, including data fusion algorithm and feature recognition technology. Also, various sensor data are adjusted. The fall detection cascade algorithm is proposed to classify data with different features in order, thereby completing target detection. Finally, combined with heart rate sensor, height sensor and microcontroller unit software and patients' e-health information, the research and development of an information collection system for fall detection are realized. Six young volunteers are selected to test the system performance. The results show that for the six testers, the heart rate detected by the ordinary device and the device of this investigation is the same when it is resting in different states of resting, walking, as well as walking and falling. The heart rate difference between walking and falling detection is not large (within the allowable error range of the device). But the best detection effect is to measure after the patient falls, which not only reduces power consumption but also keeps the detection error to a minimum. The height sensor is in the static state, increased by 75 m in the vertical direction and decreased by 75 cm from the static position in the vertical direction. The height difference of the data information exported from these three cases has some errors compared with the actual 75 cm. The tester's three situations of resting, walking and falling, standing up after sitting still and falling are observed. The waveform when resting is stable, and the acceleration information also fluctuates significantly when walking and after standing up. The accuracy of the developed system is above 80%, wh

关键词： cascade algorithm information collection system for fall detection multi-modal information fusion stroke patients

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Construction of smooth refinable function vectors by cascade algorithms

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2002年第4期40卷 1354-1368页

作者： Chen, DR Beijing Univ Aeronaut & Astronaut Dept Appl Math Beijing 100083 Peoples R China Hubei Inst Nationalities Enshi 44500 Hubei Peoples R China

This paper establishes an equivalent relation between the convergence of a cascade algorithm in Sobolev space and the convergence of an associated cascade algorithm in L-p space. It reduces the convergence in Sobolev space to that in L-p space. On the other hand, by the equivalence we present an algorithm for construction of refinement masks which generate convergent cascade algorithms in Sobolev space. It is very easy to implement the algorithm. Examples are given to illustrate the theory.

关键词： refinable function vector Sobolev space cascade algorithm factorization of mask joint spectral radius

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Multivariate Refinement Equations and Convergence of cascade algorithms in L_(p)(0

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Acta Mathematica Sinica,English Series 2003年第1期19卷 97-106页

作者： Song LI Department of Mathematices Zhejiang UniversityHangzhou 310027P.R.China Institute of Mathematics Academy of Mathematics and System sciencesChinese Academy of SciencesBeijing 100080P.R.China

We consider the solutions of refinement equations written in the form$$\varphi \left( x \right) = \sum\limits_{\alpha \in \Zopf^s} {a\left( \alpha \right)\varphi \left( {Mx - \alpha } \right) + g\left( x \right),\,\,\,x \in \Ropf^s} $$where the vector of functions } = (}1, ..., }r)T is unknown, g is a given vector of compactly supported functions on A^s, a is a finitely supported sequence of r 2 r matrices called the refinement mask, and M is an s 2 s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite interval. The cascade algorithm with mask a, g, and dilation M generates a sequence }n, n = 1, 2, ..., by the iterative process$$\varphi _n \left( x \right) = \sum\limits_{\alpha \in \Zopf^s} {a\left( \alpha \right)\varphi _{n - 1} \left(Mx - \alpha \right) + g\left( x \right),\,\,\,x \in \Ropf^s} $$from a starting vector of function }0. We characterize the Lp-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness property of the solutions of the refinement equations associated with the homogeneous refinement equation.

关键词： Inhomogeneous refinement equation Joint spectral radius cascade algorithm L_(p)(R^(s))(0

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CONVERGENCE OF cascade algorithmS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

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Chinese Annals of Mathematics,Series B 2003年第3期24卷 367-386页

作者： SUN QIYU Department of Mathematics, University of Houston, Houston, TX 77204, USA. Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, 119260, Singapore. Univ Houston Dept Math Houston TX 77204 USA Natl Univ Singapore Dept Math Singapore 119260 Singapore

In this paper, the author at first develops a method to study convergence of the cascadealgorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), andthen applies the previous result on the convergence to characterizing compactly supportedrefinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriateinitial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).

关键词： cascade algorithm cascade operator Refinable distribution Shift-invariant space Linear independent shifts Stable shifts Fractional Sobolev space

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Nonuniform cascade algorithms

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2000年第1-2期119卷 223-234页

作者： Goodman, TNT Lee, SL Univ Dundee Dept Math Dundee DD1 4HN Scotland Natl Univ Singapore Dept Math Singapore 119260 Singapore

For a sequence of bounded linear operators H-k, k = 0, 1,..., on a Banach space S, the algorithm phi(k,n) = H(k)phi(k+1,n-1) generates a family of sequences (phi(k,n))(n=0)(infinity), k = 0, 1,..., from an initial family of vectors phi(k,0) epsilon S, k = 0, 1,.... We study the convergence of phi(k,n) as n --> infinity, and give an application on the convergence of cascade algorithms for nonuniform splines when S is the space of all sequences phi:=(phi(i))(i epsilon z) with norm parallel to phi parallel to:=sup(i epsilon z)parallel to phi(i)parallel to < infinity, and phi(i), i epsilon Z, belong to the Banach space X = L-2(R). (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： Banach space cascade algorithm operator refinement equation

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Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks

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JOURNAL OF APPROXIMATION THEORY 2002年第2期119卷 133-155页

作者： Chen, DR Plonka, G Univ Duisburg Inst Math D-47048 Duisburg Germany Beijing Univ Aeronaut & Astronaut Dept Appl Math Beijing 100083 Peoples R China Hubei Inst Nationalities Dept Math Enshi 445000 Hubei Peoples R China

In this paper, the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks. (C) 2002 Elsevier Science (USA).

关键词： cascade algorithm Sobolev space joint spectral radius perturbation of refinable functions

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Stability implies convergence of cascade algorithms in Sobolev space

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2002年第1期268卷 41-52页

作者： Chen, DR Zheng, XB Beijing Univ Aeronaut & Astronaut Dept Appl Math Beijing 100083 Peoples R China Hubei Inst Nationalities Dept Math Enshi 445000 Hubei Peoples R China

This article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in Sobolev space to which the refinable function vector belongs. An ex... 详细信息

关键词： cascade algorithm Sobolev space stability Hermite interpolant

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