Obtaining sparse distributions in 2D inverse problems

Journal of Magnetic Resonance - Tập 281 - Trang 188-198 - 2017
A. Reci1, A.J. Sederman1, L.F. Gladden1
1Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, United Kingdom

Tài liệu tham khảo

Jensen, 2016, Numerical density–to–potential inversions in time–dependent density functional theory, Phys. Chem. Chem. Phys., 18, 21079, 10.1039/C6CP00312E Ivanov, 2015, Electrostatic point charge fitting as an inverse problem: revealing the underlying ill–conditioning, J. Chem. Phys., 143, 134102, 10.1063/1.4932105 Elizade, 2014, Inverse problem of capillary filling, Phys. Rev. Lett., 112, 134502, 10.1103/PhysRevLett.112.134502 Kügler, 2009, Parameter identification for chemical reaction systems using sparsity enforcing regularization: a case study for the chlorite-iodide reaction, J. Phys. Chem. A, 113, 2775, 10.1021/jp808792u An, 2008, Inverse problem in the thick–target method of measurements of inner–shell ionization cross sections by electron or positron impact, Phys. Rev. A, 77, 042702, 10.1103/PhysRevA.77.042702 Callaghan, 2011 J. Keeler, Understanding NMR Spectroscopy, Wiley, second ed., 2010. Fleury, 2016, Characterization of shales using T1–T2 maps, J. Petrol. Sci. Eng., 137, 55, 10.1016/j.petrol.2015.11.006 Weber, 2009, Comparing strengths of surface interactions for reactants and solvents in porous catalysts using two–dimensional NMR relaxation correlations, J. Phys. Chem. C, 113, 6610, 10.1021/jp811246j English, 1991, Quantitative two–dimensional time correlation relaxometry, Magnet. Reson. Med., 22, 425, 10.1002/mrm.1910220250 Hürlimann, 2002, Quantitative measurement of two–dimensional distribution functions of diffusion and relaxation in grossly inhomogeneous fields, J. Magn. Reson., 157, 31, 10.1006/jmre.2002.2567 Zhang, 2014, Spatially resolved D-T2 correlation NMR of porous media, J. Magn. Reson., 242, 41, 10.1016/j.jmr.2014.01.017 Korb, 2015, Relation and correlation between NMR relaxation times, diffusion coefficients, and viscosity of heavy crude oils, J. Phys. Chem. C, 119, 24439, 10.1021/acs.jpcc.5b07510 Lawson, 1995 A.N. Tikhonov, V.Y. Arsenin, Solutions of Ill–posed Problems, V. H. Winston and Sons, 1977. Provencher, 1982, A constrained regularization method for inverting data represented by linear algebraic or integral equations, Comput. Phys. Commun., 27, 213, 10.1016/0010-4655(82)90173-4 Provencher, 1982, CONTIN: a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations, Comput. Phys. Commun., 27, 229, 10.1016/0010-4655(82)90174-6 Borgia, 1998, Uniform–penalty inversion of multiexponential decay data, J. Magn. Reson., 122, 65, 10.1006/jmre.1998.1387 Ambrosone, 1999, General methods for determining the droplet size distribution in emulsion systems, J. Chem. Phys., 110, 797, 10.1063/1.478047 Su, 2016, An inversion method of 2D NMR relaxation spectra in low fields based on LSQR and L–curve, J. Magn. Reson., 265, 146, 10.1016/j.jmr.2016.01.024 Babak, 2017, Parsimony and goodness–of–fit in multi–dimensional NMR inversion, J. Magn. Reson., 274, 46, 10.1016/j.jmr.2016.11.005 Raj, 2014, Multi–compartment T2 relaxometry using a spatially constrained multi–Gaussian model, PLoS ONE, 9, e98391, 10.1371/journal.pone.0098391 Zheng, 2010, On the measurement of multi-component T2 relaxation in cartilage by MR spectroscopy and imaging, Magn. Reson. Imaging, 28, 537, 10.1016/j.mri.2009.12.006 Song, 2002, T1–T2 correlation spectra obtained using a fast two–dimensional Laplace inversion, J. Magn. Reson., 154, 261, 10.1006/jmre.2001.2474 Buttgereit, 2001, Simultaneous regularization method for the determination of radius distributions from experimental correlation functions, Phys. Rev. E, 64, 041404, 10.1103/PhysRevE.64.041404 Honerkamp, 1993, A nonlinear regularization method for the analysis of photon correlation spectroscopy data, J. Chem. Phys., 98, 865, 10.1063/1.464251 Whitall, 1989, Quantitative interpretation of NMR relaxation data, J. Magn. Reson., 84, 134 Song, 2005, Determining the resolution of Laplace inversion spectrum, J. Chem. Phys., 122, 104104, 10.1063/1.1858436 Candés, 2006, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inf. Theory, 52, 489, 10.1109/TIT.2005.862083 Lustig, 2007, Sparse MRI: the application of compressed sensing for rapid MR imaging, Magn. Reson. Med., 58, 1182, 10.1002/mrm.21391 Benning, 2014, Phase reconstruction from velocity–encoded MRI measurements – A survey of sparsity–promoting variational approaches, J. Magn. Reson., 238, 26, 10.1016/j.jmr.2013.10.003 Urbańczyk, 2013, Iterative thresholding algorithm for multiexponential decay applied to PGSE NMR data, Anal. Chem., 85, 1828, 10.1021/ac3032004 Bai, 2016, Fast, accurate 2D–MR relaxation exchange spectroscopy (REXSY): beyond compressed sensing, J. Chem. Phys., 145, 154202, 10.1063/1.4964144 Gamez, 2016, Compressed sensing in spectroscopy for chemical analysis, J. Anal. At. Spectrom., 31, 2165, 10.1039/C6JA00262E Rudin, 1992, Nonlinear total variation based noise removal algorithms, Physica D, 60, 259, 10.1016/0167-2789(92)90242-F Benjamini, 2016, Use of marginal distributions constrained optimization (MADCO) for accelerated 2D MRI relaxometry and diffusometry, J. Magn. Reson., 271, 40, 10.1016/j.jmr.2016.08.004 Benjamini, 2017, Towards clinically feasible relaxation–diffusion MRI using MADCO, Micropor. Mesorpor. Mat. Zhou, 2017, The inversion of 2D NMR relaxometry data using L1 regularization, J. Magn. Reson., 275, 46, 10.1016/j.jmr.2016.12.003 Cai, 2011, Orthogonal matching pursuit for sparse signal recovery with noise, IEEE Trans. Inf. Theory, 57, 4680, 10.1109/TIT.2011.2146090 Burger, 2013, An adaptive inverse scale space method for compressed sensing, Math. Comp., 82, 269, 10.1090/S0025-5718-2012-02599-3 Beck, 2009, A fast iterative shrinkage–thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., 2, 183, 10.1137/080716542 Washburn, 2006, Tracking pore to pore exchange using relaxation exchange spectroscopy, Phys. Rev. Lett., 97, 175502, 10.1103/PhysRevLett.97.175502 Song, 2016, The robust identification of exchange from T2–T2 time–domain features, J. Magn. Reson., 265, 164, 10.1016/j.jmr.2016.02.001 Callaghan, 2004, Diffusion-diffusion correlation and exchange as a signature for local order and dynamics, J. Chem. Phys., 120, 4032, 10.1063/1.1642604 Paulsen, 2014, Two–dimensional diffusion time correlation experiment using a single direction gradient, J. Magn. Reson., 244, 6, 10.1016/j.jmr.2014.04.007 Morris, 1993, Resolution of discrete and continuous molecular size distributions by means of diffusion-ordered 2D NMR spectroscopy, J. Am. Chem. Soc., 115, 4291, 10.1021/ja00063a053 E.L. Cussler, Diffusion: Mass Transfer in Fluid Systems, Cambridge University Press, third ed., 2009. Godefroy, 2001, Surface nuclear magnetic relaxation and dynamics of water and oil in macroporous media, Phys. Rev. E, 64, 021605, 10.1103/PhysRevE.64.021605 Mitchell, 2012, Numerical estimation of relaxation and diffusion distributions in two dimensions, Prog. Nucl. Magn. Reson. Spectrosc., 62, 34, 10.1016/j.pnmrs.2011.07.002 G.H. Golub, C.F. van Loan, Matrix Computations, The John Hopkins University Press, third ed., 1996. R.G. Baraniuk, Compressive sensing, IEEE Signal Process. Mag. July, 2007, 118–124. Boyd, 2004 Chambolle, 2011, A first–order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vis., 40, 120, 10.1007/s10851-010-0251-1 Carr, 1954, Effects of diffusion on free precession in Nuclear Magnetic Resonance experiments, Phys. Rev., 94, 630, 10.1103/PhysRev.94.630 Meiboom, 1958, Modified spin-echo method for measuring nuclear relaxation times, Rev. Sci. Instrum., 29, 688, 10.1063/1.1716296 Aguilar, 2012, Spin echo NMR spectra without J modulation, Chem. Commun., 48, 811, 10.1039/C1CC16699A Hahn, 1949, An accurate Nuclear Magnetic Resonance method for measuring spin–lattice relaxation times, Phys. Rev., 76, 145, 10.1103/PhysRev.76.145 Tanner, 1970, Use of the stimulated echo in NMR diffusion studies, J. Chem. Phys., 52, 2523, 10.1063/1.1673336 Venkataramanan, 2002, Solving Fredholm integrals of the first kind with tensor product structure in 2 and 2.5 dimensions, IEEE Trans. Signal Process., 50, 1017, 10.1109/78.995059 Golub, 1979, Generalized cross–validation as a method for choosing a good ridge parameter, Technometrics, 21, 215, 10.1080/00401706.1979.10489751 Gray, 1992, Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis, J. Am. Statist. Assoc., 87, 942, 10.1080/01621459.1992.10476248 Tibshirani, 1996, Regression shrinkage and selection via the Lasso, J. R. Statist. Soc. B, 58, 267 Zou, 2007, On the “degrees of freedom” of the Lasso, Ann. Statist., 35, 2173, 10.1214/009053607000000127 Tibshirani, 2012, Degrees of freedom in Lasso problems, Ann. Statist., 40, 1198, 10.1214/12-AOS1003 Dossal, 2013, The degrees of freedom of the Lasso for general design matrix, Stat. Sinica, 23, 809 Akaike, 1974, A new look at the statistical model identification, IEEE Trans. Autom. Control, 19, 716, 10.1109/TAC.1974.1100705 Schwarz, 1978, Estimating the dimension of a model, Ann. Statist., 6, 461, 10.1214/aos/1176344136 Mallows, 1973, Somme comments on Cp, Technometrics, 15, 661 Hansen, 1992, Analysis of discrete ill–posed problems by means of the L–curve, SIAM Rev., 34, 561, 10.1137/1034115 Tehrani, 2012, L1 regularization method in electrical impedance tomography by using the L1–curve (Pareto frontier curve), Appl. Math. Model., 36, 1095, 10.1016/j.apm.2011.07.055 Morozov, 1984 Norton, 1986 Babadi, 2009, Asymptotic achievability of the Cramér-Rao bound for noisy compressive sampling, IEEE Trans. Signal Process., 57, 1233, 10.1109/TSP.2008.2010379 Bickel, 2009, Simultaneous analysis of Lasso and Dantzig selector, Ann. Stat., 37, 1705, 10.1214/08-AOS620 Ben-Haim, 2010, The Cramér-Rao bound for estimating a sparse parameter vector, IEEE Trans. Signal Process., 58, 3384, 10.1109/TSP.2010.2045423 Ben-Haim, 2010, Coherence-based performance guarantees for estimating a sparse vector under random noise, IEEE Trans. Signal Process., 58, 5030, 10.1109/TSP.2010.2052460 Callaghan, 1991 Freed, 2005, Scaling laws for diffusion coefficients in mixtures of alkanes, Phys. Rev. Lett., 94, 067602, 10.1103/PhysRevLett.94.067602 Freed, 2007, Dependence on chain length of NMR relaxation times in mixtures of alkanes, J. Chem. Phys., 126, 174502, 10.1063/1.2723734