On optimization techniques for solving nonlinear inverse problems

By Eldad Haber, Uri M. Ascher, D. Oldenburg. 2000

346 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geophysics, Oceanography

View Paper: https://www.semanticscholar.org/paper/772271fe8f7331306850d48381fc5f3803cb80cd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geophysics

In Oceanography

Citations in the corpus

Efficient nonlinear predictive error variance for highly parameterized models (2006, methodology): “Regularized inversion is used widely for data interpretation [e.g., Engl et al., 1996; Haber et al., 2000; Vogel, 2002], and has seen increasing application in groundwater model calibration.”
SimPEG: An open source framework for simulation and gradient based parameter estimation in geophysical applications (2015, background): “Parker (1994); Hansen (1998)).”
INEXACT AND TRUNCATED PARAREAL-INTIME KRYLOV SUBSPACE METHODS FOR PARABOLIC OPTIMAL CONTROL PROBLEMS (2012, background): “This approach yields a KKT system with a saddle point form; see, e.g., [3] [4] [13] [14] [15] [21].”
A hybrid regularized inversion methodology for highly parameterized environmental models (2005, background): “…the adjoint state [Tsourlos and Ogilvy, 1999], and solving the large matrix equations that result from estimating a large number of parameters, such as conjugate gradients [Mackie and Madden, 1993; Haber et al., 2000] and matrix factorizations [Portniaguine, 1999; Portniaguine and Zhdanov, 2002].”
Neurobiology of Aging: Contents (2005, neutral): “• Computational fluid dynamics [213, 407, 459, 469, 499] • Constrained and weighted least squares estimation [59, 222] • Constrained optimization [210, 506, 507] • Economics [18, 143, 320, 456] • Electrical circuits and networks [51, 109, 449, 467] • Electromagnetism [67, 390, 392] • Finance [348, 3”
Electrical impedance tomography (2002, background): “Examples of such iterative algorithms can be found in [22, 51, 53, 79, 82, 108, 153] and the references within.”
A multilevel, level-set method for optimizing eigenvalues in shape design problems (2004, methodology): “Following our work [8, 2, 9] we form the Lagrangian”
Sub-Sampled Newton Methods II: Local Convergence Rates (2016, neutral): “Such second order information have long been used in many machine learning applications [6, 51, 26, 30, 11, 12] as well as many PDE constrained inverse problems [15, 41, 40, 10, 19].”
Approximate Inverse Preconditioning for Shifted Linear Systems (2003, methodology): “The test matrices are all available from the Matrix Market [16] with the exception of GEO, which is part of a problem from [11], and of DISCDIFF, which is from [15, p.”
Implementing bound constraints and total-variation regularization in extended full waveform inversion with the alternating direction method of multiplier: application to large contrast media (2019, background): “…space that encompasses the unknown wavefield and the subsurface parameters is first projected onto the parameter space by computing exactly the incident wavefields in the current subsurface model before updating this later (Haber et al., 2000; Askan et al., 2007; Epanomeritakis et al., 2008).”
Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach (2004, methodology): “Thus, in a typical iteration for given u, λ, and m, we differentiate equations 5 with respect to these variables and, dropping second-order information, obtain the following linear system of equations for the corrections δu, δλ, and δm: A 0 GQT Q AT 0 0 GT βWT W δuδλ δm = − LλLu Lm (17) (see, e”
A Preconditioner for Generalized Saddle Point Problems (2004, methodology): “Finally, we consider a saddle point problem arising in geophysics and supplied to us by Eldad Haber of Emory University; see [28, 33, 34].”
A survey on level set methods for inverse problems and optimal design (2005, methodology): “The efficient solution of this linear system for the model problems 1 and 3 has been investigated in Burger [26] using an all-at-once approach [29, 30, 65, 66], which leads to a large, sparse indefinite linear system for the velocity, a linearized state variable and a dual variable.”