Applications of Dynamic Mode Decomposition and Sparse Reconstruction in the Data-Driven Dynamic Analysis of Physical Systems

Applications of Dynamic Mode Decomposition and Sparse Reconstruction in The Data-Driven Dynamic Analysis of Physical Systems

[1]  Eric Wan.  Sigma-Point Filters: An Overview with Applications to Integrated Navigation and Vision Assisted Control , 2006, 2006 IEEE Nonlinear Statistical Signal Processing Workshop.

[2]  Mario A. Rotea,et al.  Data-driven Reduced Order Model for prediction of wind turbine wakes , 2015 .

[3]  Michael Markl,et al.  Time‐resolved three‐dimensional phase‐contrast MRI , 2003, Journal of magnetic resonance imaging : JMRI.

[4]  Gene H. Golub,et al.  Singular value decomposition and least squares solutions , 1970, Milestones in Matrix Computation.

[5]  Jinjun Wang,et al.  Divergence-free smoothing for volumetric PIV data , 2016 .

[6]  I. Mezić,et al.  Spectral analysis of nonlinear flows , 2009, Journal of Fluid Mechanics.

[7]  K. Willcox.  Unsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition , 2004 .

[8]  M. Markl,et al.  4D flow cardiovascular magnetic resonance consensus statement , 2015, Journal of Cardiovascular Magnetic Resonance.

[9]  P. Walker,et al.  Semiautomated method for noise reduction and background phase error correction in MR phase velocity data , 1993, Journal of magnetic resonance imaging : JMRI.

[10]  Michael Markl,et al.  Improved SNR in phase contrast velocimetry with five‐point balanced flow encoding , 2010, Magnetic resonance in medicine.

[11]  A. Tikhonov,et al.  Numerical Methods for the Solution of Ill-Posed Problems , 1995 .

[12]  Avipsa S. Panda,et al.  A Comparative Analysis of Compression Techniques – The Sparse Coding and BWT , 2016 .

[13]  Steven L. Brunton,et al.  Compressed sensing and dynamic mode decomposition , 2016 .

[14]  N J Pelc,et al.  Reconstructions of phase contrast, phased array multicoil data , 1994, Magnetic resonance in medicine.

[15]  M. Markl,et al.  The effect of resolution on viscous dissipation measured with 4D flow MRI in patients with Fontan circulation: Evaluation using computational fluid dynamics. , 2015, Journal of biomechanics.

[16]  P. Schmid,et al.  Dynamic mode decomposition of numerical and experimental data , 2008, Journal of Fluid Mechanics.

[17]  Ahmadreza Baghaie,et al.  Dynamic Denoising and Gappy Data Reconstruction Based on Dynamic Mode Decomposition and Discrete Cosine Transform , 2018, Applied Sciences.

[18]  A. H. Andersen,et al.  Analysis of noise in phase contrast MR imaging. , 1996, Medical physics.

[19]  Clarence W. Rowley,et al.  A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition , 2014, Journal of Nonlinear Science.

[20]  Frank Ong,et al.  Robust 4D flow denoising using divergence‐free wavelet transform , 2015, Magnetic resonance in medicine.

[21]  David L. Donoho,et al.  The Optimal Hard Threshold for Singular Values is 4/sqrt(3) , 2013, 1305.5870.

[22]  George E. Karniadakis,et al.  A Reconstruction Method for Gappy and Noisy Arterial Flow Data , 2007, IEEE Transactions on Medical Imaging.

[23]  Ahmadreza Baghaie,et al.  Curvelet Transform-based volume fusion for correcting signal loss artifacts in Time-of-Flight Magnetic Resonance Angiography data , 2018, Comput. Biol. Medicine.

[24]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[25]  Barbara M. Johnston,et al.  Non-Newtonian blood flow in human right coronary arteries: steady state simulations. , 2004, Journal of biomechanics.

[26]  Mojtaba F. Fathi,et al.  Tribological study in microscale using 3D SEM surface reconstruction , 2016 .

[27]  Alfred O. Hero,et al.  Shrinkage estimation of high dimensional covariance matrices , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[28]  Michael Markl,et al.  Towards high‐resolution 4D flow MRI in the human aorta using kt‐GRAPPA and B1+ shimming at 7T , 2016, Journal of magnetic resonance imaging : JMRI.

[29]  Konstantin Nikolaou,et al.  MR Image Reconstruction Using a Combination of Compressed Sensing and Partial Fourier Acquisition: ESPReSSo , 2016, IEEE Transactions on Medical Imaging.

[30]  Steven L. Brunton,et al.  On dynamic mode decomposition: Theory and applications , 2013, 1312.0041.

[31]  Alastair J. Martin,et al.  Numerical simulations of flow in cerebral aneurysms: comparison of CFD results and in vivo MRI measurements. , 2008, Journal of biomechanical engineering.

[32]  Show-Ling Jang,et al.  Size and location of ruptured intracranial aneurysms. , 2009, Journal of Korean Neurosurgical Society.

[33]  B. Wranne,et al.  Temporally resolved 3D phase‐contrast imaging , 1996, Magnetic resonance in medicine.

[34]  J. Hennig,et al.  Optimized pre-processing of time-resolved 2 D and 3 D Phase Contrast MRI data , 2007 .

[35]  J. Hennig,et al.  Quantitative 2D and 3D phase contrast MRI: Optimized analysis of blood flow and vessel wall parameters , 2008, Magnetic resonance in medicine.

[36]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[37]  Sebastian Kozerke,et al.  Reconstruction of divergence‐free velocity fields from cine 3D phase‐contrast flow measurements , 2013, Magnetic resonance in medicine.

[38]  Lawrence Sirovich,et al.  Karhunen–Loève procedure for gappy data , 1995 .

[39]  N J Pelc,et al.  Concomitant gradient terms in phase contrast MR: Analysis and correction , 1998, Magnetic resonance in medicine.

[40]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[41]  Q. Xiang,et al.  Temporal phase unwrapping for cine velocity imaging , 1995, Journal of magnetic resonance imaging : JMRI.

[42]  Kaare Brandt Petersen,et al.  The Matrix Cookbook , 2006 .

[43]  Charles A Mistretta,et al.  Transstenotic pressure gradients: measurement in swine--retrospectively ECG-gated 3D phase-contrast MR angiography versus endovascular pressure-sensing guidewires. , 2007, Radiology.

[44]  G. Kerschen,et al.  The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview , 2005 .

[45]  Valérie Perrier,et al.  Divergence-free and curl-free wavelets in two dimensions and three dimensions: application to turbulent flows , 2006 .

[46]  Peter J. Schmid,et al.  Sparsity-promoting dynamic mode decomposition , 2012, 1309.4165.

[47]  Matthew O. Williams,et al.  A kernel-based method for data-driven koopman spectral analysis , 2016 .

[48]  C. Striebel,et al.  On the maximum likelihood estimates for linear dynamic systems , 1965 .

[49]  Ahmadreza Baghaie,et al.  Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression. , 2017, Journal of biomechanics.

[50]  Vincent Crocher,et al.  Modifying Kinect placement to improve upper limb joint angle measurement accuracy. , 2016, Journal of hand therapy : official journal of the American Society of Hand Therapists.

[51]  Alastair J. Martin,et al.  Phase‐contrast magnetic resonance imaging measurements in intracranial aneurysms in vivo of flow patterns, velocity fields, and wall shear stress: Comparison with computational fluid dynamics , 2009, Magnetic resonance in medicine.

[52]  Michael Unser,et al.  Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data , 2015, IEEE Signal Processing Letters.

[53]  Krishna S. Nayak,et al.  Computational fluid dynamics simulations of blood flow regularized by 3D phase contrast MRI , 2015, Biomedical engineering online.

[54]  Ahmadreza Baghaie,et al.  Denoising and spatial resolution enhancement of 4D flow MRI using proper orthogonal decomposition and lasso regularization , 2018, Comput. Medical Imaging Graph..

[55]  Stuart M Grieve,et al.  Use of multi‐velocity encoding 4D flow MRI to improve quantification of flow patterns in the aorta , 2016, Journal of magnetic resonance imaging : JMRI.

[56]  Michael Markl,et al.  k‐t GRAPPA accelerated four‐dimensional flow MRI in the aorta: Effect on scan time, image quality, and quantification of flow and wall shear stress , 2014, Magnetic resonance in medicine.

[57]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[58]  J. Junkins,et al.  Optimal Estimation of Dynamic Systems , 2004 .

[59]  P. Holmes,et al.  The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows , 1993 .

[60]  A.H. Haddad,et al.  Applied optimal estimation , 1976, Proceedings of the IEEE.

[61]  Ron Kohavi,et al.  A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection , 1995, IJCAI.

[62]  A. Barakat,et al.  Unsteady and three-dimensional simulation of blood flow in the human aortic arch. , 2002, Journal of biomechanical engineering.

[63]  F. Guéniat,et al.  A dynamic mode decomposition approach for large and arbitrarily sampled systems , 2015 .

[64]  Clarence W. Rowley,et al.  Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition , 2014, Experiments in Fluids.

[65]  Nico Westerhof,et al.  In Vivo Validation of Magnetic Resonance Blood Volume Flow Measurements with Limited Spatial Resolution in Small Vessels , 1995, Magnetic resonance in medicine.

[66]  Clarence W. Rowley,et al.  Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses , 2012, J. Nonlinear Sci..

[67]  Jianfeng Gao,et al.  Scalable training of L1-regularized log-linear models , 2007, ICML '07.

[68]  Katja Bachmeier,et al.  Numerical Heat Transfer And Fluid Flow , 2016 .

[69]  Michael Unser,et al.  Variational enhancement and denoising of flow field images , 2011, 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[70]  G. Glover,et al.  Generalized reconstruction of phase contrast MRI: Analysis and correction of the effect of gradient field distortions , 2003, Magnetic resonance in medicine.

[71]  A. Chatterjee.  An introduction to the proper orthogonal decomposition , 2000 .

[72]  S. Ravindran.  A reduced-order approach for optimal control of fluids using proper orthogonal decomposition , 2000 .

[73]  Leah R. Enders,et al.  The extent of altered digit force direction correlates with clinical upper extremity impairment in chronic stroke survivors. , 2015, Journal of biomechanics.

[74]  N J Pelc,et al.  Noise reduction in three‐dimensional phase‐contrast MR velocity measurementsl , 1993, Journal of magnetic resonance imaging : JMRI.