@article{Akcelik2002,
author = {Akcelik, Volkan and Biros, George and Ghattas, Omar},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/ghattas\_TV.pdf:pdf},
isbn = {076951524X},
journal = {Supercomputing, ACM/IEEE \ldots},
number = {c},
pages = {1--15},
title = {{Parallel multiscale Gauss-Newton-Krylov methods for inverse wave propagation}},
url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1592877},
volume = {00},
year = {2002}
}
@article{Aravkin2012,
abstract = {Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. The structure of these problems allows efficient optimization strategies—a well-known example is variable projection , where nonlinear least-squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood and maximum a posteriori likelihood problems with nuisance parameters, such as variance or degrees of freedom (d.o.f.). As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, d.o.f. parameter estimation in the context of robust inverse problems, and automatic calibration. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large-scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.},
archivePrefix = {arXiv},
arxivId = {1206.6532},
author = {Aravkin, Aleksandr Y and van Leeuwen, Tristan},
eprint = {1206.6532},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/nuisance\_param.pdf:pdf},
journal = {Inverse Problems},
month = jun,
number = {11},
pages = {115016},
title = {{Estimating nuisance parameters in inverse problems}},
url = {http://arxiv.org/abs/1206.6532},
volume = {28},
year = {2012}
}
@article{Aravkin2011,
abstract = {We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such problems motivates dimensionality reduction techniques based on randomly mixing experiments. These techniques break down, however, when robust data-fitting formulations are used, which are essential in cases of missing data, unusually large errors, and systematic features in the data unexplained by the forward model. We survey robust methods within a statistical framework, and propose a semistochastic optimization approach that allows dimensionality reduction. The efficacy of the methods are demonstrated for a large-scale seismic inverse problem using the robust Student's t-distribution, where a useful synthetic velocity model is recovered in the extreme scenario of 60\% data missing at random. The semistochastic approach achieves this recovery using 20\% of the effort required by a direct robust approach.},
archivePrefix = {arXiv},
arxivId = {1110.0895},
author = {Aravkin, Aleksandr and Friedlander, Michael P. and van Leeuwen, Tristan},
doi = {10.1007/s10107-012-0571-6},
eprint = {1110.0895},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/robust\_inversion.pdf:pdf},
journal = {Mathematical \ldots},
keywords = {inverse problems,robust,seismic inversion,stochastic optimization},
month = oct,
title = {{Robust inversion via semistochastic dimensionality reduction}},
url = {http://link.springer.com/article/10.1007/s10107-012-0571-6 http://arxiv.org/abs/1110.0895},
year = {2011}
}
@book{Bertsekas1999,
author = {Bertsekas, Dimitri P.},
isbn = {1886529000},
pages = {780},
publisher = {Athena Scientific; 2nd edition},
title = {{Nonlinear Programming}},
url = {http://www.amazon.com/Nonlinear-Programming-Dimitri-P-Bertsekas/dp/1886529000/ref=sr\_1\_2?ie=UTF8\&qid=1395180760\&sr=8-2\&keywords=nonlinear+programming},
year = {1999}
}
@article{Chambolle2011,
author = {Chambolle, Antonin and Pock, Thomas},
file = {:D$\backslash$:/Dropbox/docs/math/slim/amp/pd\_alg\_final.pdf:pdf},
journal = {Journal of Mathematical Imaging and Vision},
title = {{A first-order primal-dual algorithm for convex problems with applications to imaging}},
url = {http://link.springer.com/article/10.1007/s10851-010-0251-1},
year = {2011}
}
@article{Chung2005,
author = {Chung, Eric T. and Chan, Tony F. and Tai, Xue-Cheng},
doi = {10.1016/j.jcp.2004.11.022},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/Chung-Chan-Tai-jcp-04.pdf:pdf},
issn = {00219991},
journal = {Journal of Computational Physics},
month = may,
number = {1},
pages = {357--372},
title = {{Electrical impedance tomography using level set representation and total variational regularization}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021999104004711},
volume = {205},
year = {2005}
}
@article{Esser2013,
author = {Esser, Ernie and Lou, Yifei and Xin, Jack},
doi = {10.1137/13090540X},
file = {:D$\backslash$:/Dropbox/docs/math/slim/ernweb/90540.pdf:pdf},
issn = {1936-4954},
journal = {SIAM Journal on Imaging Sciences},
keywords = {basis pursuit,difference of convex programming,differential optical absorption spec-,hyperspectral imaging,nonnegative least squares,scaled gradient projec-,structured sparsity,tion,unmixing},
month = jan,
number = {4},
pages = {2010--2046},
title = {{A Method for Finding Structured Sparse Solutions to Nonnegative Least Squares Problems with Applications}},
url = {http://epubs.siam.org/doi/abs/10.1137/13090540X},
volume = {6},
year = {2013}
}
@article{Esser2010,
author = {Esser, Ernie and Zhang, Xiaoqun and Chan, Tony F.},
doi = {10.1137/09076934X},
file = {:D$\backslash$:/Dropbox/docs/math/slim/ernweb/76934.pdf:pdf},
issn = {1936-4954},
journal = {SIAM Journal on Imaging Sciences},
keywords = {convex optimization,l 1,operator splitting,primal-dual methods,total variation minimization},
month = jan,
number = {4},
pages = {1015--1046},
title = {{A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science}},
url = {http://epubs.siam.org/doi/abs/10.1137/09076934X},
volume = {3},
year = {2010}
}
@article{He2012,
author = {He, Bingsheng and Yuan, X},
file = {:D$\backslash$:/Dropbox/docs/math/slim/amp/HeYuan-SIIMS-2nd.pdf:pdf},
journal = {SIAM Journal on Imaging Sciences},
keywords = {contraction method,dual method,image restoration,primal-,proximal point algorithm,saddle-point problem,total variation},
pages = {1--35},
title = {{Convergence analysis of primal-dual algorithms for a saddle-point problem: from contraction perspective}},
url = {http://epubs.siam.org/doi/abs/10.1137/100814494},
year = {2012}
}
@article{Herrmann2013,
author = {Herrmann, Felix J. and Hanlon, Ian and Kumar, Rajiv and van Leeuwen, Tristan and Li, Xiang and Smithyman, Brendan and Wason, Haneet and Calvert, Andrew J. and Javanmehri, Mostafa and Takougang, Eric Takam},
doi = {10.1190/tle32091082.1},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/frugal\_fwi.pdf:pdf},
issn = {1070-485X},
journal = {The Leading Edge},
month = sep,
number = {9},
pages = {1082--1092},
title = {{Frugal full-waveform inversion: From theory to a practical algorithm}},
url = {http://library.seg.org/doi/abs/10.1190/tle32091082.1},
volume = {32},
year = {2013}
}
@book{Nocedal1999,
abstract = {Despite application of cryogen spray (CS) precooling, customary treatment of port wine stain (PWS) birthmarks with a single laser pulse does not result in complete lesion blanching for a majority of patients. One obvious reason is nonselective absorption by epidermal melanin, which limits the maximal safe radiant exposure. Another possible reason for treatment failure is screening of laser light within large PWS vessels, which prevents uniform heating of the entire vessel lumen. Our aim is to identify the parameters of sequential CS cooling and laser irradiation that will allow optimal photocoagulation of various PWS blood vessels with minimal risk of epidermal thermal damage.},
author = {Nocedal, J and Wright, S J},
booktitle = {Analysis},
chapter = {5},
doi = {10.1002/lsm.21040},
editor = {Glynn, Peter and Robinson, Stephen M},
isbn = {0387987932},
issn = {10969101},
number = {2},
pages = {164--75},
pmid = {21384397},
publisher = {Springer},
series = {Springer Series in Operations Research},
title = {{Numerical Optimization}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21643320},
volume = {43},
year = {1999}
}
@article{Rudin1992,
author = {Rudin, LI and Osher, S and Fatemi, E},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/PhysicaRudinOsher.pdf:pdf},
journal = {Physica D: Nonlinear Phenomena},
pages = {259--268},
title = {{Nonlinear total variation based noise removal algorithms}},
url = {http://www.sciencedirect.com/science/article/pii/016727899290242F},
volume = {60},
year = {1992}
}
@article{Tarantola1984,
author = {Tarantola, Albert},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/InversionOfSeismic.pdf:pdf},
journal = {Geophysics},
number = {8},
pages = {1259--1266},
title = {{Inversion of seismic reflection data in the acoustic approximation}},
url = {http://link.springer.com/article/10.1007/s10107-012-0571-6 http://arxiv.org/abs/1110.0895 http://library.seg.org/doi/abs/10.1190/1.1441754},
volume = {49},
year = {1984}
}
@article{VandenBerg2011,
author = {van den Berg, Ewout and Friedlander, Michael P.},
doi = {10.1137/100785028},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/2011BergFriedlander.pdf:pdf},
issn = {1052-6234},
journal = {SIAM Journal on Optimization},
keywords = {10,100785028,1137,49m29,65k05,90c06,90c25,ams subject classifications,basis pursuit,completion,compressed sensing,convex program,doi,duality,group sparsity,matrix,newton,root-finding,s method,sparse solutions},
month = oct,
number = {4},
pages = {1201--1229},
title = {{Sparse Optimization with Least-Squares Constraints}},
url = {http://epubs.siam.org/doi/abs/10.1137/100785028},
volume = {21},
year = {2011}
}
@article{VanLeeuwen2013,
abstract = {Wave-equation based inversions, such as full-waveform inversion, are challenging because of their computational costs, memory requirements, and reliance on accurate initial models. To confront these issues, we propose a novel formulation of full-waveform inversion based on a penalty method. In this formulation, the objective function consists of a data-misfit term and a penalty term which measures how accurately the wavefields satisfy the wave-equation. Because we carry out the inversion over a larger search space, including both the model and synthetic wavefields, our approach suffers less from local minima. Our main contribution is the development of an efficient optimization scheme that avoids having to store and update the wavefields by explicit elimination. Compared to existing optimization strategies for full-waveform inversion, our method differers in two main aspects; i) The wavefields are solved from an augmented wave-equation, where the solution is forced to solve the wave-equation and fit the observed data, ii) no adjoint wavefields are required to update the model, which leads to significant computational savings. We demonstrate the validity of our approach by carefully selected examples and discuss possible extensions and future research.},
author = {van Leeuwen, T. and Herrmann, F. J.},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/vanLeeuwen2013Penalty1.pdf:pdf},
journal = {Geophysical Journal International},
keywords = {computa-,controlled source seismology,inverse theory,seismic tomography},
number = {1},
pages = {661--667},
title = {{Mitigating local minima in full-waveform inversion by expanding the search space}},
url = {http://gji.oxfordjournals.org/cgi/doi/10.1093/gji/ggt258},
volume = {195},
year = {2013}
}
@article{Leeuwen,
author = {van Leeuwen, T. and Herrmann, F. J.},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/vanLeeuwen2013Penalty2.pdf:pdf},
title = {{A penalty method for PDE-constrained optimization}},
year = {2013}
}
@article{VanLeeuwen2013a,
author = {van Leeuwen, Tristan and Herrmann, Felix J.},
doi = {10.1111/j.1365-2478.2012.01096.x},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/fastFWI.pdf:pdf},
issn = {00168025},
journal = {Geophysical Prospecting},
keywords = {full-waveform inversion,source-encoding,stochastic optimization},
month = jun,
number = {2010},
pages = {10--19},
title = {{Fast waveform inversion without source-encoding}},
url = {http://doi.wiley.com/10.1111/j.1365-2478.2012.01096.x},
volume = {61},
year = {2013}
}
@article{Virieux2009,
author = {Virieux, J. and Operto, S.},
doi = {10.1190/1.3238367},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/GPY\_2009\_VIRIEUX.pdf:pdf},
issn = {0016-8033},
journal = {Geophysics},
month = nov,
number = {6},
pages = {WCC1--WCC26},
title = {{An overview of full-waveform inversion in exploration geophysics}},
url = {http://library.seg.org/doi/abs/10.1190/1.3238367},
volume = {74},
year = {2009}
}
@article{Zhang2010a,
author = {Zhang, Xiaoqun and Burger, Martin and Osher, Stanley},
doi = {10.1007/s10915-010-9408-8},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/cam09-99.pdf:pdf},
issn = {0885-7474},
journal = {Journal of Scientific Computing},
keywords = {1 minimization,49k35,49m37,49n15,65k10,90c25,ams subjects,bregman iteration,inexact,proximal point iteration,saddle point,uzawa methods},
month = aug,
number = {1},
pages = {20--46},
title = {{A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration}},
url = {http://link.springer.com/10.1007/s10915-010-9408-8},
volume = {46},
year = {2010}
}
@article{Zhu2008,
author = {Zhu, Mingqiang and Chan, Tony},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/AMP/cam08-34.pdf:pdf},
journal = {UCLA CAM Report [08-34]},
number = {1},
pages = {1--29},
title = {{An Efficient Primal-Dual Hybrid Gradient Algorithm For Total Variation Image Restoration}},
year = {2008}
}