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

作者：Lu, Ling; Xu, Wei^*; Qiao, Sanzheng

来源：Numerical Algorithms, 2015, 69(4): 875-891.

DOI：10.1007/s11075-014-9930-0

• Multi-level Block Hankel Matrix
• SVD
• Cadzow filtering
• Seismic data processing

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.

• 出版日期2015-8
• 单位同济大学