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Efficient generalized Golub–Kahan based methods for dynamic inverse problems

Julianne Chung, Arvind K Saibaba, Matthew Brown, Erik Westman
2018 Inverse Problems  
Numerical examples from photoacoustic tomography, deblurring, and passive seismic tomography demonstrate the range of applicability and effectiveness of the described approaches.  ...  Compared to static inverse problems, incorporating prior information in both space and time in a Bayesian framework can become computationally intensive, in part, due to the large number of unknown parameters  ...  Acknowledgements We would like to acknowledge Creighton mines for providing the raw data for the PST application.  ... 
doi:10.1088/1361-6420/aaa0e1 fatcat:ash6cdfilbclzjem63tas6cqz4

Randomized algorithms for Generalized Hermitian Eigenvalue Problems with application to computing Karhunen-Loève expansion [article]

Arvind K. Saibaba, Jonghyun Lee, Peter K. Kitanidis
2015 arXiv   pre-print
The error analysis shows that the randomized algorithm is most accurate when the generalized singular values of B^-1A decay rapidly.  ...  Additionally, we derive some new results that provide insight into the accuracy of the eigenvalue calculations.  ...  to a Fourier series representation of a function.  ... 
arXiv:1307.6885v3 fatcat:p2hjdzwqljbqzjt4eveiy6dq5i

Computational methods for large-scale inverse problems: a survey on hybrid projection methods [article]

Julianne Chung, Silvia Gazzola
2021 arXiv   pre-print
Although the idea of a hybrid Krylov method for linear inverse problems goes back to the 1980s, several recent advances on new regularization frameworks and methodologies have made this field ripe for  ...  In this paper, we provide a practical and accessible introduction to hybrid projection methods in the context of solving large (linear) inverse problems.  ...  In addition to requiring the user to predefine these additional parameters for the hyperpriors, a potential computational disadvantage of this approach is that the posterior (4.32) is no longer Gaussian  ... 
arXiv:2105.07221v2 fatcat:vviylanambfmjheocl7e5k3bnq

Two New Nonlinear Nonlocal Diffusions for Noise Reduction

Patrick Guidotti, James V. Lambers
2008 Journal of Mathematical Imaging and Vision  
The presence of nontrivial equilibria also explains why blurring is kept in check. One of the models has been proved to be well-posed.  ...  understood and do not lead to any "paradox".  ...  Typically G σ is a Gaussian and σ determines the scale beyond which regularization occurs. This approach goes back to [9] but also see [1, 20] .  ... 
doi:10.1007/s10851-008-0108-z fatcat:yawk27t7y5hxzp7tsits46tj4i

Image Segmentation Using Markov Random Field Model in Fully Parallel Cellular Network Architectures

Tamás Szirányi, Josiane Zerubia, LászLó Czúni, David Geldreich, Zoltán Kato
2000 Real-time imaging  
M arkovian approaches to early vision processes need a huge amount of computing power. These algorithms can usually be implemented on parallel computing structures.  ...  Herein, we show that the Markovian labeling approach can be implemented in fully parallel cellular network architectures, using simple functions and data representations.  ...  Acknowledgements This work was partially supported by``Balaton'' programme of the National Committee for Technological Development, Hungary and the French Ministry of Foreign Aairs and by the Hungarian  ... 
doi:10.1006/rtim.1998.0159 fatcat:fr7fdhjl3nhsvb573zla6wzlqm

On Regularizing Effects of MINRES and MR-II for Large-Scale Symmetric Discrete Ill-Posed Problems [article]

Yi Huang, Zhongxiao Jia
2016 arXiv   pre-print
uses explicit regularization within projected problems is needed to compute a best possible regularized solution to a given ill-posed problem; (iii) the kth iterate by MINRES is more accurate than the  ...  For large scale symmetric discrete ill-posed problems, MINRES and MR-II are often used iterative regularization solvers.  ...  of the Gaussian point spread function and thus the amount of smoothing.  ... 
arXiv:1503.03936v3 fatcat:32h6hyugkbhmxg4hcfhh4a7vsi

The Regularization Theory of the Krylov Iterative Solvers LSQR, CGLS, LSMR and CGME For Linear Discrete Ill-Posed Problems [article]

Zhongxiao Jia
2016 arXiv   pre-print
We also analyze the regularization of the other two Krylov solvers LSMR and CGME, proving that LSMR has similar regularizing effects to LSQR for each kind of problem and both are superior to CGME.  ...  For the large-scale linear discrete ill-posed problem Ax-b or Ax=b with b contaminated by a white noise, Lanczos bidiagonalization based LSQR and its mathematically equivalent CGLS are most commonly used  ...  Yanfei Yang for running the numerical experiments. I am grateful to ProfessorsÅ. Björck, P. C. Hansen, L.  ... 
arXiv:1608.05907v2 fatcat:znhztmib6nbgbbfif7ouhsxqwi

A Proximal Point Analysis of the Preconditioned Alternating Direction Method of Multipliers

Kristian Bredies, Hongpeng Sun
2017 Journal of Optimization Theory and Applications  
In the last two sections, we present applications in order to demonstrate the efficiency of the preconditioning approaches for ADMM. Finally, we give a brief conclusion.  ...  Classical approaches for the convergence analysis of the ADMM method usually involve convex duality.  ...  Such approaches have been pursued for the PDRQ method in [21] and lead to competitive algorithms for TV-regularized L 2 -and L 1 -deblurring.  ... 
doi:10.1007/s10957-017-1112-5 fatcat:hbl6kgcllnaixiqzugeknsihn4

Inpainting and Zooming Using Sparse Representations

M.J. Fadili, J.-L. Starck, F. Murtagh
2008 Computer journal  
We also suggest some guidelines to automatically tune the regularization parameter.  ...  The EM framework gives a principled way to establish formally the idea that missing samples can be recovered/ interpolated based on sparse representations.  ...  ACKNOWLEDGEMENTS We would like to thank deeply Miki Elad and Dave Donoho for very interesting and stimulating discussions.  ... 
doi:10.1093/comjnl/bxm055 fatcat:brvru5pedzailhzawyctrlsioq

A Deconvolution Framework with Applications in Medical and Biological Imaging

Steffen Remmele
2012
Many deblurring methods were proposed to restore these images in the last decade which are part of the deconvolution framework.  ...  In this thesis, a dose reconstruction method based on PET images which reverses the convolution approach is presented and the potential to reconstruct the actually delivered dose distribution from measured  ...  Acknowledgement First and foremost, I would like to thank my doctoral adviser Jürgen Hesser for giving  ... 
doi:10.11588/heidok.00013452 fatcat:ujlxkadan5happdkhw45bfjjhy

A depth-derived Pleistocene age model: Uncertainty estimates, sedimentation variability, and nonlinear climate change

Peter Huybers, Carl Wunsch
2004 Paleoceanography  
The ocean mixing times for the d 18 O signal can range out to 1000 years and longer [Wunsch, 2003b] . Imposing simultaneity between d 18 O events, if correct, deblurs this mixing effect.  ...  non-Gaussian, or both (nonlinear records are usually non-Gaussian).  ... 
doi:10.1029/2002pa000857 fatcat:x6ywjxg62nck7httcxclnrr5qi

Quantum State Tomography of an Itinerant Squeezed Microwave Field

F. Mallet, M. A. Castellanos-Beltran, H. S. Ku, S. Glancy, E. Knill, K. D. Irwin, G. C. Hilton, L. R. Vale, K. W. Lehnert
2011 Physical Review Letters  
We use a second JPA as a pre-amplifier to improve the quantum efficiency of the field quadrature measurement (QM) from 2% to 36 +/- 4%.  ...  Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 69 +/- 8% of the variance of the vacuum.  ...  The authors acknowledge support from the DARPA/ MTO QuEST program. Note added.-A different method was recently used to obtain a similar state reconstruction [30] .  ... 
doi:10.1103/physrevlett.106.220502 pmid:21702586 fatcat:pkm7sz47jvdjdivsl2erm2ip5y

Statistical physics of linear and bilinear inference problems [article]

Christophe Schülke
2016 arXiv   pre-print
To this end, it uses belief propagation, thanks to which high-dimensional distributions can be sampled efficiently, thus making a Bayesian approach to inference tractable.  ...  The recent development of compressed sensing has led to spectacular advances in the understanding of sparse linear estimation problems as well as in algorithms to solve them.  ...  Despite the gross error of taking a discrete prior for a continuous distribution, taking a high enough discretization n d of the interval allows approaching performances of a calibrated algorithm.  ... 
arXiv:1607.00675v1 fatcat:jw4fq7svxvfpvgsm4rob6pa2fm

Higher-order total variation approaches and generalisations [article]

Kristian Bredies, Martin Holler
2019 arXiv   pre-print
Over the last decades, the total variation (TV) evolved to one of the most broadly-used regularisation functionals for inverse problems, in particular for imaging applications.  ...  A major part of this review is finally concerned with presenting examples and applications where higher-order TV approaches turned out to be beneficial.  ...  Here, the approach is often to acquire highly subsampled data, possibly combined with gating techniques, such that motion consistency can be assumed for each single frame of a time series of measurements  ... 
arXiv:1912.01587v1 fatcat:l2bxra2uh5h7hn7ebda4ngz5lq

A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution [article]

Qing Qu, Xiao Li, Zhihui Zhu
2020 arXiv   pre-print
}_i=1^p up to a signed shift ambiguity.  ...  Our theoretical results are corroborated by numerical experiments, which demonstrate superior performance of the proposed approach over the previous methods on both synthetic and real datasets.  ...  We would like to thank the National Science  ... 
arXiv:1908.10776v3 fatcat:ku5mxr7ppfhejlh6kdyuuppspm
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