[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 Jiasong^{1, 3}, Yang Guanyu^{1, 3}, Lotfi Senahdji^{2, 3}, Shu Huazhong^{1, 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 Senahdji^{2, 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]

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