TY - JOUR
ID - 65881
TI - Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation
JO - Journal of the Earth and Space Physics
JA - JESPHYS
LA - en
SN - 2538-371X
AU - Vatankhah, Saeed
AD - Assistant Professor, Department of Earth Physics, Institute of Geophysics, University of Tehran, Iran
Y1 - 2018
PY - 2018
VL - 44
IS - 4
SP - 29
EP - 39
KW - Magnetic survey
KW - Sparse inversion
KW - Golub-Kahan bidiagonalization
KW - Regularization parameter estimation
KW - Truncated generalized cross validation
DO - 10.22059/jesphys.2018.247879.1006954
N2 - In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that projects the problem onto a Krylov subspace with a significantly reduced dimension. The model matrix of the projected system inherits the ill-conditioning of the original matrix, but the spectrum of the projected system accurately captures only a portion of the full spectrum. Equipped with the singular value decomposition of the projected system matrix, the solution of the projected problem is expressed using a filtered singular value expansion. This expansion depends on a regularization parameter which is determined using the method of Generalized Cross Validation (GCV), but here it is used for the truncated spectrum. This new technique, Truncated GCV (TGCV), is more effective compared with the standard GCV method. Numerical results using a synthetic example and real data demonstrate the efficiency of the presented algorithm.
UR - https://jesphys.ut.ac.ir/article_65881.html
L1 - https://jesphys.ut.ac.ir/article_65881_6379712cc0856924f302337e3f0a59a9.pdf
ER -