A fast SVD for multilevel block Hankel matrices with minimal memory storage

被引:0
|
作者
Ling Lu
Wei Xu
Sanzheng Qiao
机构
[1] Tongji University,Department of Mathematics
[2] McMaster University,Department of Computing and Software
来源
Numerical Algorithms | 2015年 / 69卷
关键词
Multi-level Block Hankel Matrix; SVD; Cadzow filtering; Seismic data processing; 15B05; 15A18; 65F20; 65F25; 65F50;
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摘要
Motivated by the Cadzow filtering in seismic data processing, this paper presents a fast SVD method for multilevel block Hankel matrices. A seismic data presented as a multidimensional array is first transformed into a two dimensional multilevel block Hankel (MBH) matrix. Then the Lanczos process is applied to reduce the MBH matrix into a bidiagonal or tridiagonal matrix. Finally, the SVD of the reduced matrix is computed using the twisted factorization method. To achieve high efficiency, we propose a novel fast MBH matrix-vector multiplication method for the Lanczos process. In comparison with existing fast Hankel matrix-vector multiplication methods, our method applies 1-D, instead of multidimensional, FFT and requires minimum storage. Moreover, a partial SVD is performed on the reduced matrix, since complete SVD is not required by the Caszow filtering. Our numerical experiments show that our fast MBH matrix-vector multiplication method significantly improves both the computational cost and storage requirement. Our fast MBH SVD algorithm is particularly efficient for large size multilevel block Hankel matrices.
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页码:875 / 891
页数:16
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