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049 _aN$TA
245 0 0 _aLarge scale inverse problems :
_bcomputational methods and applications in the earth sciences /
_cedited by Mike Cullen, Melina A. Freitag, Stefan Kindermann, Robert Scheichl.
264 1 _aBerlin ;
_aBoston :
_bDe Gruyter,
_c[2013]
264 4 _c©2013
300 _a1 online resource (ix, 203 pages) :
_billustrations
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aRadon Series on Computational and Applied Mathematics
504 _aIncludes bibliographical references.
505 0 _aPreface; Synergy of inverse problems and data assimilation techniques; 1 Introduction; 2 Regularization theory; 3 Cycling, Tikhonov regularization and 3DVar; 4 Error analysis; 5 Bayesian approach to inverse problems; 6 4DVar; 7 Kalman filter and Kalman smoother; 8 Ensemble methods; 9 Numerical examples; 9.1 Data assimilation for an advection-diffusion system; 9.2 Data assimilation for the Lorenz-95 system; 10 Concluding remarks; Variational data assimilation for very large environmental problems; 1 Introduction; 2 Theory of variational data assimilation.
505 8 _a2.1 Incremental variational data assimilation3 Practical implementation; 3.1 Model development; 3.2 Background error covariances; 3.3 Observation errors; 3.4 Optimization methods; 3.5 Reduced order approaches; 3.6 Issues for nested models; 3.7 Weak-constraint variational assimilation; 4 Summary and future perspectives; Ensemble filter techniques for intermittent data assimilation; 1 Bayesian statistics; 1.1 Preliminaries; 1.2 Bayesian inference; 1.3 Coupling of random variables; 1.4 Monte Carlo methods; 2 Stochastic processes; 2.1 Discrete time Markov processes.
505 8 _a2.2 Stochastic difference and differential equations2.3 Ensemble prediction and sampling methods; 3 Data assimilation and filtering; 3.1 Preliminaries; 3.2 SequentialMonte Carlo method; 3.3 Ensemble Kalman filter (EnKF); 3.4 Ensemble transform Kalman-Bucy filter; 3.5 Guided sequential Monte Carlo methods; 3.6 Continuous ensemble transform filter formulations; 4 Concluding remarks; Inverse problems in imaging; 1 Mathematicalmodels for images; 2 Examples of imaging devices; 2.1 Optical imaging; 2.2 Transmission tomography; 2.3 Emission tomography; 2.4 MR imaging; 2.5 Acoustic imaging.
505 8 _a2.6 Electromagnetic imaging3 Basic image reconstruction; 3.1 Deblurring and point spread functions; 3.2 Noise; 3.3 Reconstruction methods; 4 Missing data and prior information; 4.1 Prior information; 4.2 Undersampling and superresolution; 4.3 Inpainting; 4.4 Surface imaging; 5 Calibration problems; 5.1 Blind deconvolution; 5.2 Nonlinear MR imaging; 5.3 Attenuation correction in SPECT; 5.4 Blind spectral unmixing; 6 Model-based dynamic imaging; 6.1 Kinetic models; 6.2 Parameter identification; 6.3 Basis pursuit; 6.4 Motion and deformation models; 6.5 Advanced PDE models.
505 8 _aThe lost honor of l2-based regularization1 Introduction; 2 l1-based regularization; 3 Poor data; 4 Large, highly ill-conditioned problems; 4.1 Inverse potential problem; 4.2 The effect of ill-conditioning on L1 regularization; 4.3 Nonlinear, highly ill-posed examples; 5 Summary; List of contributors.
520 _aThis book is thesecond volume of three volume series recording the ""Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment"" taking place in Linz, Austria, October 3-7, 2011. The volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications.
588 0 _aPrint version record.
542 1 _fThis work is licensed under a Creative Commons license
_uhttps://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
546 _aEnglish.
506 0 _aOpen Access
_5EbpS
650 0 _aInverse problems (Differential equations)
650 7 _aApplied mathematics.
_2bicssc
_9381
650 7 _aMATHEMATICS
_xCalculus.
_2bisacsh
_928352
650 7 _aMATHEMATICS
_xMathematical Analysis.
_2bisacsh
_928353
650 7 _aInverse problems (Differential equations)
_2fast
_0(OCoLC)fst00978098
655 0 _aElectronic books.
655 4 _aElectronic books.
700 1 _aCullen, Michael J. P.,
_eeditor.
_928354
700 1 _aFreitag, Melina A.,
_d1980-
_eeditor.
_928355
700 1 _aKindermann, Stefan,
_d1972-
_eeditor.
_928356
700 1 _aScheichl, Robert,
_d1972-
_eeditor.
_928357
776 0 8 _iPrint version:
_aScheichl, Robert.
_tLarge Scale Inverse Problems : Computational Methods and Applications in the Earth Sciences.
_dBerlin : De Gruyter, ©2013
_z9783110282221
830 0 _aRadon series on computational and applied mathematics.
_96267
856 4 0 _3EBSCOhost
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