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浙江大学学报(工学版)
浙江大学学报(工学版)  2014, Vol. 48 Issue (4): 748-785    DOI: 10.3785/j.issn.1008-973X.2014.04.027
地球科学     
位场数据重构的lp范数稀疏约束正则化方法
陈国新, 陈生昌
浙江大学 地球科学系,浙江 杭州 310027
Regularization method with  p-norm sparsity constraints for potential field data reconstruction
CHEN Guo-xin, CHEN Sheng-chang
Department of Earth Sciences, Zhejiang University, Hangzhou 310027, China
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摘要：

基于位场数据在离散余弦变换域的稀疏性,利用lp(0≤p<1）范数代替l1范数作为模型参数稀疏性的度量.引入lp范数稀疏约束正则化方法,借用迭代再加权最小二乘算法思想求解得到稀疏约束优化问题的解.分析不同p值的lp范数稀疏约束正则化方法的数据重构能力.将该算法应用于实际位场数据重构试验中获得了较理想的结果,通过边界外延加大计算区域的方法减少了边界数据的重构误差,提高了数据重构质量.
Abstract:

The  p-norm (0≤p<1) was used to replace the  1-norm to measure the model parameters sparsity based on the sparseness of the potential field data in the discrete cosine transform domain. The regularization method with p-norm sparsity constraints was introduced. Then the iteratively re-weighted least squares algorithm was used to get the analytic expression of the corresponding optimization problem. The reconstruction ability of regularization method for different lp-norm sparsity constraints was analyzed. The algorithm was applied to actual potential field data reconstruction and the ideal result was obtained. The reconstruction error of boundary data was reduced by expanding the calculated area via boundary extension, and the quality of the reconstructed data was improved.
出版日期: 2014-09-03
:  P 631  
基金资助:

国家自然科学基金资助项目（41074133）.
通讯作者: 陈生昌,男,教授,博导.     E-mail: chenshengc@zju.edu.cn
作者简介: 陈国新（1988—）,男,博士生,从事地球物理反演方法及应用的研究.E-mail: zjucgx@zju.edu.cn
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引用本文:

陈国新, 陈生昌. 位场数据重构的lp范数稀疏约束正则化方法[J]. 浙江大学学报(工学版), 2014, 48(4): 748-785.

CHEN Guo-xin, CHEN Sheng-chang. Regularization method with  p-norm sparsity constraints for potential field data reconstruction. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2014, 48(4): 748-785.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2014.04.027    或    http://www.zjujournals.com/eng/CN/Y2014/V48/I4/748

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