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Volumn 211, Issue 2, 2011, Pages 178-185

On the inversion of diffusion NMR data: Tikhonov regularization and optimal choice of the regularization parameter

Author keywords

Diffusion NMR; Inverse Laplace transform; Inversion; Parameter choice; Tikhonov regularization

Indexed keywords

DIFFUSION NMR; INVERSE LAPLACE TRANSFORM; INVERSION; PARAMETER CHOICE; TIKHONOV REGULARIZATION;

EID: 79960700535     PISSN: 10907807     EISSN: 10960856     Source Type: Journal    
DOI: 10.1016/j.jmr.2011.05.014     Document Type: Article
Times cited : (74)

References (48)
  • 1
    • 33646376290 scopus 로고
    • Spin diffusion measurements: Spin echos in the presence of a time-dependent field gradient
    • E.O. Stejskal, and J.E. Tanner Spin diffusion measurements: spin echos in the presence of a time-dependent field gradient J. Chem. Phys. 42 1965 288 292
    • (1965) J. Chem. Phys. , vol.42 , pp. 288-292
    • Stejskal, E.O.1    Tanner, J.E.2
  • 2
    • 36849101148 scopus 로고
    • Use of the stimulated echo in NMR diffusion studies
    • J.E. Tanner Use of the stimulated echo in NMR diffusion studies J. Chem. Phys. 52 1970 2523 2526
    • (1970) J. Chem. Phys. , vol.52 , pp. 2523-2526
    • Tanner, J.E.1
  • 4
    • 0347359145 scopus 로고    scopus 로고
    • Diffusion ordered nuclear magnetic resonance spectroscopy: Principles and applications
    • C.S. Johnson Diffusion ordered nuclear magnetic resonance spectroscopy: principles and applications Prog. NMR. Spectrosc. 34 1999 203 256
    • (1999) Prog. NMR. Spectrosc. , vol.34 , pp. 203-256
    • Johnson, C.S.1
  • 6
    • 33846881569 scopus 로고    scopus 로고
    • Solid- and solution-state structures of indium 'alkene analogues'
    • DOI 10.1039/b616747k
    • M.S. Hill, P.B. Hitchcock, and R. Pongtavornpinyo Solid- and solution-state structures of indium 'alkene analogues' Dalton Trans. 2007 731 733 (Pubitemid 46217759)
    • (2007) Dalton Transactions , Issue.7 , pp. 731-733
    • Hill, M.S.1    Hitchcock, P.B.2    Pongtavornpinyo, R.3
  • 8
    • 33646547271 scopus 로고    scopus 로고
    • Biexponential fitting of diffusion-ordered NMR data: Practicalities and limitations
    • DOI 10.1021/ac060034a
    • M. Nilsson, M.A. Connell, A.L. Davis, and G.A. Morris Biexponential fitting of diffusion-ordered NMR data: practicalities and limitations Anal. Chem. 78 2006 3040 3045 (Pubitemid 43726123)
    • (2006) Analytical Chemistry , vol.78 , Issue.9 , pp. 3040-3045
    • Nilsson, M.1    Connell, M.A.2    Davis, A.L.3    Morris, G.A.4
  • 9
    • 0001494550 scopus 로고    scopus 로고
    • Multivariate Image Analysis of Magnetic Resonance Images with the Direct Exponential Curve Resolution Algorithm (DECRA): Part 1: Algorithm and Model Study
    • W. Windig, J.P. Hornak, and B. Antalek Multivariate image analysis of magnetic resonance images with the direct exponential curve resolution algorithm (DECRA) Part 1: algorithm and model study J. Magn. Reson. 132 1998 298 306 (Pubitemid 128450730)
    • (1998) Journal of Magnetic Resonance , vol.132 , Issue.2 , pp. 298-306
    • Windig, W.1    Hornak, J.P.2    Antalek, B.3
  • 10
    • 0032087380 scopus 로고    scopus 로고
    • Multivariate Image Analysis of Magnetic Resonance Images with the Direct Exponential Curve Resolution Algorithm (DECRA): Part 2: Application to Human Brain Images
    • B. Antalek, J.P. Hornak, and W. Windig Multivariate image analysis of magnetic resonance images with the direct curve resolution algorithm (DECRA) Part 2: application to human brain images J. Magn. Reson. 132 1998 307 315 (Pubitemid 128450731)
    • (1998) Journal of Magnetic Resonance , vol.132 , Issue.2 , pp. 307-315
    • Antalek, B.1    Hornak, J.P.2    Windig, W.3
  • 11
    • 0030134645 scopus 로고    scopus 로고
    • Global least-squares analysis of large, correlated spectral data sets: Application to component-resolved FT-PGSE NMR spectroscopy
    • P. Stilbs, K. Paulsen, and P.C. Griffiths Global least-squares analysis of large, correlated spectral data sets: application to component-resolved FT-PGSE NMR spectroscopy J. Phys. Chem. 100 1996 8180 8189 (Pubitemid 126789182)
    • (1996) Journal of Physical Chemistry , vol.100 , Issue.20 , pp. 8180-8189
    • Stilbs, P.1    Paulsen, K.2    Griffiths, P.C.3
  • 12
    • 0029905872 scopus 로고    scopus 로고
    • Generalized rank annihilation method applied to a single multicomponent pulsed gradient spin echo NMR data set
    • DOI 10.1021/ja962172v, PII S0002786396021725
    • B. Antalek, and W. Windig Generalized rank annihilation method applied to a single multicomponent pulsed gradient spin echo NMR data set J. Am. Chem. Soc. 118 1996 10331 10332 (Pubitemid 26375231)
    • (1996) Journal of the American Chemical Society , vol.118 , Issue.42 , pp. 10331-10332
    • Antalek, B.1    Windig, W.2
  • 13
    • 43949126524 scopus 로고    scopus 로고
    • Speedy component resolution: An improved tool for processing diffusion-ordered spectroscopy data
    • DOI 10.1021/ac7025833
    • M. Nilsson, and G.A. Morris Speedy component resolution: an improved tool for processing diffusion-ordered spectroscopy data Anal. Chem. 80 2008 3777 3782 (Pubitemid 351705881)
    • (2008) Analytical Chemistry , vol.80 , Issue.10 , pp. 3777-3782
    • Nilsson, M.1    Morris, G.A.2
  • 14
    • 0001409990 scopus 로고    scopus 로고
    • Maximum entropy processing of DOSY NMR spectra
    • M.A. Delsuc, and T.E. Malliavin Maximum entropy processing of DOSY NMR spectra Anal. Chem. 70 1998 2146 2148
    • (1998) Anal. Chem. , vol.70 , pp. 2146-2148
    • Delsuc, M.A.1    Malliavin, T.E.2
  • 16
    • 33747876344 scopus 로고    scopus 로고
    • Diffusion coefficient distribution from NMR-DOSY experiments using Hopfield neural network
    • DOI 10.1016/j.jmr.2006.06.005, PII S1090780706001510, Thrid Annual Focus on Safety
    • R.C.O. Sebastiao, C.N. Pacheco, J.P. Braga, and D. Pilo-Vesolo Diffusion coefficient distribution from NMR-DOSY experiments using Hopfield neural network J. Magn. Reson. 182 2006 22 28 (Pubitemid 44293431)
    • (2006) Journal of Magnetic Resonance , vol.182 , Issue.1 , pp. 22-28
    • Sebastiao, R.C.O.1    Pacheco, C.N.2    Braga, J.P.3    Pilo-Veloso, D.4
  • 17
    • 0011887937 scopus 로고
    • Determination of molecular weight distributions for polymers by diffusion-ordered NMR
    • A. Chen, D. Wu, and C.S. Johnson Determination of molecular weight distributions for polymers by diffusion-ordered NMR J. Am. Chem. Soc. 117 1995 7965 7970
    • (1995) J. Am. Chem. Soc. , vol.117 , pp. 7965-7970
    • Chen, A.1    Wu, D.2    Johnson, C.S.3
  • 18
    • 0034817491 scopus 로고    scopus 로고
    • On the numerical inversion of the Laplace transform for nuclear magnetic resonance relaxometry
    • DOI 10.1088/0266-5611/17/1/307
    • P. Barone, A. Ramponi, and G. Sebastiani On the numerical inversion of the Laplace transform for nuclear magnetic resonance relaxometry Inverse Probl. 17 2001 77 94 (Pubitemid 32873047)
    • (2001) Inverse Problems , vol.17 , Issue.1 , pp. 77-94
    • Barone, P.1    Ramponi, A.2    Sebastiani, G.3
  • 22
    • 57049132042 scopus 로고    scopus 로고
    • Quantifying uncertainty in NMR T2 spectra using Monte Carlo inversion
    • M. Prange, and Y.-Q. Song Quantifying uncertainty in NMR T2 spectra using Monte Carlo inversion J. Magn. Reson. 196 2009 54 60
    • (2009) J. Magn. Reson. , vol.196 , pp. 54-60
    • Prange, M.1    Song, Y.-Q.2
  • 23
    • 0000673856 scopus 로고
    • Resolution of discrete and continuous molecular size distributions by means of diffusion-ordered 2D NMR spectroscopy
    • K.F. Morris, and C.S. Johnson Resolution of discrete and continuous molecular size distributions by means of diffusion-ordered 2D NMR spectroscopy J. Am. Chem. Soc. 115 1993 4291 4299
    • (1993) J. Am. Chem. Soc. , vol.115 , pp. 4291-4299
    • Morris, K.F.1    Johnson, C.S.2
  • 25
    • 0020176708 scopus 로고
    • A constrained regularization method for inverting data represented by linear algebraic or integral equations
    • S.W. Provencher A constrained regularization method for inverting data represented by linear algebraic or integral equations Comput. Phys. Commun. 27 1982 229 242
    • (1982) Comput. Phys. Commun. , vol.27 , pp. 229-242
    • Provencher, S.W.1
  • 26
    • 0642334046 scopus 로고    scopus 로고
    • A fast non-negativity-constrained least squares algorithm
    • R. Bro, and S. de Jong A fast non-negativity-constrained least squares algorithm J. Chemometr. 11 1997 393 401 (Pubitemid 127478570)
    • (1997) Journal of Chemometrics , vol.11 , Issue.5 , pp. 393-401
    • Bro, R.1    De Jong, S.2
  • 27
    • 0041708442 scopus 로고    scopus 로고
    • Inverse methods in two-dimensional NMR spectral analysis
    • J.D. van Beek, B.H. Meier, and H. Schaefer Inverse methods in two-dimensional NMR spectral analysis J. Magn. Reson. 162 2003 141 157
    • (2003) J. Magn. Reson. , vol.162 , pp. 141-157
    • Van Beek, J.D.1    Meier, B.H.2    Schaefer, H.3
  • 28
    • 11344285129 scopus 로고    scopus 로고
    • The determination of pair distance distributions by pulsed ESR using Tikhonov regularization
    • DOI 10.1016/j.jmr.2004.10.012, PII S1090780704003532
    • Y.-W. Chiang, P.P. Borbat, and J.H. Freed The determination of pair distance distributions by pulsed EPR using Tikhonov regularization J. Magn. Reson. 172 2005 279 295 (Pubitemid 40072533)
    • (2005) Journal of Magnetic Resonance , vol.172 , Issue.2 , pp. 279-295
    • Chiang, Y.-W.1    Borbat, P.P.2    Freed, J.H.3
  • 29
    • 34249781983 scopus 로고    scopus 로고
    • Determination of radical re-encounter probability distributions from magnetic field effects on reaction yields
    • DOI 10.1021/ja068209l
    • C.T. Rodgers, S.A. Norman, K.B. Henbest, C.R. Timmel, and P.J. Hore Determination of radical re-encounter probability distributions from magnetic field effects on reaction yields J. Am. Chem. Soc. 129 2007 6746 6755 (Pubitemid 46847516)
    • (2007) Journal of the American Chemical Society , vol.129 , Issue.21 , pp. 6746-6755
    • Rodgers, C.T.1    Norman, S.A.2    Henbest, K.B.3    Timmel, C.R.4    Hore, P.J.5
  • 32
    • 17444364136 scopus 로고    scopus 로고
    • Determining the resolution of Laplace inversion spectrum
    • Y.-Q. Song, L. Venkataramanan, and L. Burcaw Determining the resolution of Laplace inversion spectrum J. Chem. Phys. 122 2005 104104
    • (2005) J. Chem. Phys. , vol.122 , pp. 104104
    • Song, Y.-Q.1    Venkataramanan, L.2    Burcaw, L.3
  • 33
    • 0000570697 scopus 로고
    • Analysis of discrete ill-posed problems by means of the L-curve
    • P.C. Hansen Analysis of discrete ill-posed problems by means of the L-curve SIAM Rev. 34 1992 561 580
    • (1992) SIAM Rev. , vol.34 , pp. 561-580
    • Hansen, P.C.1
  • 34
    • 36448976249 scopus 로고    scopus 로고
    • Regularization tools version 4.0 for Matlab 7.3
    • P.C. Hansen Regularization tools version 4.0 for Matlab 7.3 Numer. Algorithms 46 2007 189 194
    • (2007) Numer. Algorithms , vol.46 , pp. 189-194
    • Hansen, P.C.1
  • 36
    • 13344267706 scopus 로고
    • Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
    • P.C. Hansen Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems Numer. Algorithms 6 1994 1 35
    • (1994) Numer. Algorithms , vol.6 , pp. 1-35
    • Hansen, P.C.1
  • 39
    • 28844467199 scopus 로고    scopus 로고
    • Aggregation behavior and chromonic liquid crystal properties of an anionic monoazo dye
    • V.R. Horowitz, L.A. Janowitz, A.L. Modic, P.A. Heiney, and P.J. Collings Aggregation behavior and chromonic liquid crystal properties of an anionic monoazo dye Phys. Rev. E 72 2005 041710
    • (2005) Phys. Rev. e , vol.72 , pp. 041710
    • Horowitz, V.R.1    Janowitz, L.A.2    Modic, A.L.3    Heiney, P.A.4    Collings, P.J.5
  • 41
    • 77955334648 scopus 로고    scopus 로고
    • NMR characterization of the aggregation state of the azo dye sunset yellow in the isotropic phase
    • M.P. Renshaw, and I.J. Day NMR characterization of the aggregation state of the azo dye sunset yellow in the isotropic phase J. Phys. Chem. B 114 2010 10032 10038
    • (2010) J. Phys. Chem. B , vol.114 , pp. 10032-10038
    • Renshaw, M.P.1    Day, I.J.2
  • 43
    • 34548564168 scopus 로고    scopus 로고
    • Evidence of wormlike micellar behavior in chromonic liquid crystals: Rheological, X-ray, and dielectric studies
    • DOI 10.1021/jp073190
    • S.K. Prasad, G.G. Nair, G. Hegde, and V. Jayalakshmi Evidence of wormlike micellar behaviour in chromonic liquid crystals: rheological, X-ray and dielectric studies J. Phys. Chem. B 111 2007 9741 9746 (Pubitemid 47387854)
    • (2007) Journal of Physical Chemistry B , vol.111 , Issue.33 , pp. 9741-9746
    • Prasad, S.K.1    Nair, G.G.2    Hegde, G.3    Jayalakshmi, Y.4
  • 44
    • 0034105749 scopus 로고    scopus 로고
    • The influence of polymer molecular-weight distributions on pulsed field gradient nuclear magnetic resonance self-diffusion experiments
    • DOI 10.1007/s003960050532
    • B. Hakansson, M. Nyden, and O. Soderman The influence of polymer molecular weight distributions on pulsed gradient nuclear magnetic resonance self-diffusion measurements Colloid Polym. Sci. 278 2000 399 405 (Pubitemid 30312862)
    • (2000) Colloid and Polymer Science , vol.278 , Issue.5 , pp. 399-405
    • Hakansson, B.1    Nyden, M.2    Soderman, O.3


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