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[1] Zhang Xu, Wu Jiasong, Yang Guanyu, et al. L1-norm minimization for quaternion signals [J]. Journal of Southeast University (English Edition), 2013, 29 (1): 33-37. [doi:10.3969/j.issn.1003-7985.2013.01.007]
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L1-norm minimization for quaternion signals()
基于L1范数正则化的四元数信号重建
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
29
Issue:
2013 1
Page:
33-37
Research Field:
Computer Science and Engineering
Publishing date:
2013-03-20

Info

Title:
L1-norm minimization for quaternion signals
基于L1范数正则化的四元数信号重建
Author(s):
Zhang Xu1 Wu Jiasong1 3 Yang Guanyu1 3 Lotfi Senahdji2 3 Shu Huazhong1 3
1Laboratory of Image Science and Technology, Southeast University, Nanjing 210096, China
2LTSI, INSERM U 1099, Université de Rennes 1, Rennes 35000, France
3Centre de Recherche en Information Biomédicale Sino-français, Nanjing 210096, China
张旭1 伍家松1 3 杨冠羽1 3 Lotfi Senahdji2 3 舒华忠1 3
1东南大学影像科学与技术实验室, 南京 210096; 2LTSI, INSERM U 1099, Université de Rennes 1, Rennes 35000, France; 3中法生物医学信息研究中心, 南京 210096
Keywords:
quaternion signal recovery compressed sensing
四元数 信号重建 压缩感知
PACS:
TP391
DOI:
10.3969/j.issn.1003-7985.2013.01.007
Abstract:
An algorithm for recovering the quaternion signals in both noiseless and noise contaminated scenarios by solving an L1-norm minimization problem is presented. The L1-norm minimization problem over the quaternion number field is solved by converting it to an equivalent second-order cone programming problem over the real number field, which can be readily solved by convex optimization solvers like SeDuMi. Numerical experiments are provided to illustrate the effectiveness of the proposed algorithm. In a noiseless scenario, the experimental results show that under some practically acceptable conditions, exact signal recovery can be achieved. With additive noise contamination in measurements, the experimental results show that the proposed algorithm is robust to noise. The proposed algorithm can be applied in compressed-sensing-based signal recovery in the quaternion domain.
提出了一种通过求解L1范数最小化问题来重建四元数信号的算法, 并且同时考虑了有噪声和没有噪声2种应用场景.该算法首先将四元数域的L1范数最小化问题转化为实数域的二次锥规划问题, 然后通过工具包如SeDuMi来解决这个二次锥规划问题.为了验证所提出算法的正确性和有效性, 进行了相关的数值试验.试验结果表明:在没有噪声的情况下, 在某些实际可接受的条件下原始信号的精确重建是可以实现的;在有噪声的情况下, 所提出的算法对于测量中的加性噪声具有鲁棒性.该算法可以被应用于四元数域基于压缩感知理论的信号重建中.

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Memo

Memo:
Biographies: Zhang Xu(1984—), male, graduate; Shu Huazhong(corresponding author), male, doctor, professor, shu.list@seu.edu.cn.
Foundation items: The National Basic Research Program of China(973 program)(No. 2011CB707904), the National Natural Science Foundation of China(No. 61073138, 61271312, 61201344, 81101104, 60911130370), the Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China(No. 20110092110023, 20120092120036), the Natural Science Foundation of Jiangsu Province(No.BK2012329, BK2012743).
Citation: Zhang Xu, Wu Jiasong, Yang Guanyu, et al. L1-norm minimization for quaternion signals[J].Journal of Southeast University(English Edition), 2013, 29(1):33-37.[doi:10.3969/j.issn.1003-7985.2013.01.007]
Last Update: 2013-03-20