3-D Projected L1 inversion of gravity data using truncated unbiased predictive risk estimator for regularization parameter estimation

[1]  Jiajia Sun,et al.  Adaptive Lp inversion for simultaneous recovery of both blocky and smooth features in a geophysical model , 2014 .

[2]  Rosemary A. Renaut,et al.  A Newton root-finding algorithm for estimating the regularization parameter for solving ill-conditioned least squares problems , 2009 .

[3]  Gene H. Golub,et al.  Generalized cross-validation as a method for choosing a good ridge parameter , 1979, Milestones in Matrix Computation.

[4]  R. Blakely Potential theory in gravity and magnetic applications , 1996 .

[5]  Michael A. Saunders,et al.  LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares , 1982, TOMS.

[6]  Elena Cherkaev,et al.  Non-smooth gravity problem with total variation penalization functional , 2002 .

[7]  Douglas W. Oldenburg,et al.  3-D inversion of magnetic data , 1996 .

[8]  K. Kubik,et al.  Compact gravity inversion , 1983 .

[9]  P. Hansen Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion , 1987 .

[10]  J. Nagy,et al.  A weighted-GCV method for Lanczos-hybrid regularization. , 2007 .

[11]  M. Chouteau,et al.  Constraints in 3D gravity inversion , 2001 .

[12]  D. Oldenburg,et al.  3-D inversion of gravity data , 1998 .

[13]  Rosemary A. Renaut,et al.  Computational Statistics and Data Analysis , 2022 .

[14]  Mark Pilkington,et al.  3D magnetic data-space inversion with sparseness constraints , 2009 .

[15]  D. Oldenburg,et al.  Subspace linear inverse method , 1994 .

[16]  D. Oldenburg,et al.  NON-LINEAR INVERSION USING GENERAL MEASURES OF DATA MISFIT AND MODEL STRUCTURE , 1998 .

[17]  Zhongxiao Jia,et al.  Some results on the regularization of LSQR for large-scale discrete ill-posed problems , 2015, 1503.01864.

[18]  Michael S. Zhdanov,et al.  Minimum support nonlinear parametrization in the solution of a 3D magnetotelluric inverse problem , 2004 .

[19]  Michel Chouteau,et al.  3D gravity inversion using a model of parameter covariance , 2003 .

[20]  Gene H. Golub,et al.  Matrix computations , 1983 .

[21]  Iveta Hn The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data , 2009 .

[22]  Rosemary A. Renaut,et al.  Hybrid and iteratively reweighted regularization by unbiased predictive risk and weighted GCV for projected systems 5 December 2016 , 2016 .

[23]  D. Oldenburg,et al.  Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method , 2003 .

[24]  Jonathan B. Ajo-Franklin,et al.  Applying Compactness Constraints to Differential Traveltime Tomography , 2007 .

[25]  J. Navarro-Pedreño Numerical Methods for Least Squares Problems , 1996 .

[26]  T. Dahlin,et al.  A comparison of smooth and blocky inversion methods in 2D electrical imaging surveys , 2001 .

[27]  S. Voronin Regularization of Linear Systems with Sparsity Constraints with Applications to Large Scale Inverse Problems , 2012 .

[28]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[29]  Bernd Hofmann,et al.  Regularization for applied inverse and ill-posed problems : a numerical approach , 1986 .

[30]  Michael S. Zhdanov,et al.  Focusing geophysical inversion images , 1999 .

[31]  Mark Pilkington,et al.  3-D Magnetic Data-space Inversion With Sparseness Constraints , 2008 .

[32]  V. Morozov On the solution of functional equations by the method of regularization , 1966 .

[33]  Per Christian Hansen,et al.  Regularization Tools version 4.0 for Matlab 7.3 , 2007, Numerical Algorithms.

[34]  Rosemary A Renaut,et al.  Regularization parameter estimation for underdetermined problems by the χ 2 principle with application to 2D focusing gravity inversion , 2014, 1402.3365.

[35]  M. Fedi,et al.  Invariant models in the inversion of gravity and magnetic fields and their derivatives , 2014 .

[36]  D. Oldenburg,et al.  A comparison of automatic techniques for estimating the regularization parameter in non-linear inverse problems , 2004 .

[37]  S. K. Runcorn,et al.  Interpretation theory in applied geophysics , 1965 .

[38]  Rosemary A. Renaut,et al.  Application of the χ2 principle and unbiased predictive risk estimator for determining the regularization parameter in 3-D focusing gravity inversion , 2014, 1408.0712.

[39]  Michael A. Saunders,et al.  Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems , 1982, TOMS.

[40]  D. Oldenburg,et al.  3-D inversion of gravity data , 1998 .

[41]  Brendt Wohlberg,et al.  An Iteratively Reweighted Norm Algorithm for Minimization of Total Variation Functionals , 2007, IEEE Signal Processing Letters.

[42]  Colin Farquharson,et al.  Constructing piecewise-constant models in multidimensional minimum-structure inversions , 2008 .

[43]  C. Vogel Computational Methods for Inverse Problems , 1987 .

[44]  Rosemary A. Renaut,et al.  Automatic estimation of the regularization parameter in 2-D focusing gravity inversion: an application to the Safo manganese mine in northwest of Iran , 2013, ArXiv.

[45]  James G. Nagy,et al.  Generalized Arnoldi-Tikhonov Method for Sparse Reconstruction , 2014, SIAM J. Sci. Comput..

[46]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[47]  Donald W. Marquaridt Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation , 1970 .

[48]  Gary D. Egbert,et al.  An efficient data-subspace inversion method for 2-D magnetotelluric data , 2000 .

[49]  P. Hansen Discrete Inverse Problems: Insight and Algorithms , 2010 .

[50]  D. Oldenburg,et al.  Generalized subspace methods for large-scale inverse problems , 1993 .