Sparse Bayesian learning for the Laplace transform inversion in dynamic light scattering

Journal of Computational and Applied Mathematics

Volumn 235, Issue 8, 2011, Pages 2861-2872

  Nyeo, Su Long ^a   Ansari, Rafat R ^b  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b NASA GLENN RESEARCH CENTER   (United States)

Author keywords

Cataract; Dynamic light scattering; Laplace transform inversion; Ocular tissues; Particle size distribution; Regularization method; Sparse Bayesian learning

Indexed keywords

CATARACT; LAPLACE TRANSFORM INVERSION; OCULAR TISSUE; REGULARIZATION METHODS; SPARSE BAYESIAN LEARNING;

ALGORITHMS; BAYESIAN NETWORKS; DYNAMIC LIGHT SCATTERING; DYNAMIC LOADS; HISTOLOGY; INVERSE PROBLEMS; LAPLACE TRANSFORMS; LENSES; MATHEMATICAL TRANSFORMATIONS; OPACITY; OPTICAL INSTRUMENTS; OPTIMIZATION; PARAMETERIZATION; PARTICLE SIZE; PARTICLE SIZE ANALYSIS; REFRACTION; SCATTERING; SIZE DISTRIBUTION;

AGGLOMERATION;

EID: 79251596155     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2010.12.008     Document Type: Article

References (39)

1. B. Chu Laser Light Scattering: Basic Principles and Practice 2nd ed. 1991 Academic Press, Inc. Boston
2. R. Xu Particle Characterization: Light Scattering Methods 2000 Springer-Verlag Netherlands
3. M. Van Laethem, B. Babusiaux, A. Neelens, and J. Clauwaert Photon correlation spectroscopy of light scattered by eye lenses in in vivo conditions Biophysical J. 59 2 1991 433 444
4. R.R. Ansari, and M.B. Datiles III Use of dynamic light scattering and Scheimpflug imaging for the early detection of cataracts Diabetes Technol. Therapeutics 1 2 1999 159 168
5. R.R. Ansari Ocular static and dynamic light scattering: a noninvasive diagnostic tool for eye research and clinical practice J. Biomed. Opt. 9 1 2004 22 37
6. R.S. Stock, and W.H. Ray Interpretation of photon correlation spectroscopy data: a comparison of analysis methods J. Polym. Sci.: Polym. Phys. Ed. 23 7 1985 1393 1447
7. S.W. Provencher CONTIN: a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations Comput. Phys. Commun. 27 3 1982 229 242
8. J. Skilling, and R.K. Bryan Maximum entropy image reconstruction: general algorithm Mon. Not. R. Astron. Soc. 211 1 1984 111 124
9. A.K. Livesey, P. Licinio, and M. Delaye Maximum entropy analysis of quasielastic light scattering from colloidal dispersions J. Chem. Phys. 84 9 1984 5102 5107
10. S.-L. Nyeo, and B. Chu Maximum-entropy analysis of photon correlation spectroscopy data Macromolecules 22 10 1989 3998 4009
11. C.-D. Sun, Z. Wang, G. Wu, and B. Chu An improvement on maximum entropy analysis of photon correlation spectroscopy data Macromolecules 25 3 1992 1114 1120
12. R.K. Bryan Maximum entropy analysis of oversampled data problems Eur. Biophys. J. 18 3 1990 165 174
13. J. Langowski, and R. Bryan Maximum entropy analysis of photon correlation spectroscopy data using a Bayesian estimate for the regularization parameter Macromolecules 24 23 1991 6346 6348
14. R. Campagna, L. D'Amore, and A. Murli An efficient algorithm for regularization of Laplace transform inversion in real case J. Comput. Appl. Math. 210 12 2007 84 98
15. S. Cuomo, L. D'Amore, and A. Murli Error analysis of a collocation method for numerically inverting a Laplace transform in case of real samples J. Comput. Appl. Math. 210 12 2007 149 158
16. B. Davies, and B. Martin Numerical inversion of the Laplace transform: a survey and comparison of methods J. Comput. Phys. 33 1 1979 1 32
17. H.L. Seal A note on the use of Laguerre polynomials in the inversion of Laplace transforms Bltter der DGVFM 12 2 1975 131 134
18. M.E. Tipping Sparse Bayesian learning and the relevance vector machine J. Mach. Learn. Res. 1 2001 211 244
19. S.-L. Nyeo, and R.R. Ansari Early cataract detection by dynamic light scattering with sparse Bayesian learning J. Innov. Opt. Health Sci. 2 3 2009 303 313
20. J.G. McWhirter, and E.R. Pike On the numerical inversion of the Laplace transform and similar equations of the first kind J. Phys. A: Math. Gen. 11 9 1978 1729 1745
21. N. Ostrowsky, D. Sornette, P. Parker, and E.R. Pike Exponential sampling method for light scattering polydispersity analysis J. Mod. Optics 28 8 1981 1059 1070
22. M. Bertero, P. Boccacci, and E.R. Pike On the recovery and resolution of exponential relaxation rates from experimental data: a singular-value analysis of the Laplace transform inversion in the presence of noise Proc. R. Soc. Lond. A 383 1784 1982 15 29
23. M. Bertero, P. Boccacci, and E.R. Pike On the recovery and resolution of exponential relaxation rates from experimental data II. The optimal choice of experimental sampling points for Laplace transform inversion Proc. R. Soc. Lond. A 393 1804 1984 51 65
24. P.J. McCarthy Direct analytic model of the L-curve for Tikhonov regularization parameter selection Inverse Problems 19 3 2003 643 663
25. P.C. Hansen Regularization tools version 4.0 for Matlab 7.3 Numer. Algorithms 46 2 2007 189 194
26. L. Reichel, and H. Sadok A new L-curve for ill-posed problems J. Comput. Appl. Math. 219 2 2008 493 508
27. V.N. Vapnik Statistical Learning Theory 1998 Wiley New York
28. D.P. Wipf, and B.D. Rao Sparse Bayesian learning for basis selection IEEE Trans. Signal Process. 52 8 2004 2153 2164
29. S.K. Majumder, N. Ghosh, and P.K. Gupta Relevance vector machine for optical diagnosis of cancer Lasers Surg. Med. 36 4 2005 323 333
30. J.T. Flake, Application of the relevance vector machine to canal flow prediction in the Sevier River basin. M.Sc. Thesis, Utah State University, Logan, Utah, 2007.
31. J.-Y. Peng, J.A.D. Aston, R.N. Gunn, C.-Y. Liou, and J. Ashburner Dynamic positron emission tomography data-driven analysis using sparse Bayesian learning IEEE Trans. Med. Imag. 27 9 2008 1356 1369
32. D.J.C. MacKay The evidence framework applied to classification networks Neural Comput. 4 5 1992 720 736
33. A.C. Faul, and M.E. Tipping Analysis of sparse Bayesian learning T.G. Dietterich, S. Becker, Z. Ghahramani, Advances in Neural Information Processing Systems, 14 2002 MIT Press 383 389
34. G. Rodriguez, and D. Theis An algorithm for estimating the optimal regularization parameter by the L-curve Rend. Mat., Serie VII 25 1 2005 69 84
35. V.A. Morozov On the solution of functional equations by the method of regularization Sov. Math. Dokl. 7 1966 414 417
36. O. Scherzer The use of Morozov's discrepancy principle for Tikhonov regularization for solving nonlinear ill-posed problems Computing 51 1 1993 45 60
37. R. Arcangeli Pseudo-solution de l'quation Ax = y C.R. Acad. Sci. Paris Sr. A 263 8 1966 282 285
38. C.W. Groetsch, and J. Guacaneme Arcangeli's method for Fredholm equations of the first kind Proc. Amer. Math. Soc. 99 2 1987 256 260
39. M.B. Datiles III, R.R. Ansari, K.I. Suh, S. Vitale, G.F. Reed, J.S. Zigler Jr., and F.L. Ferris III Clinical detection of precataractous lens protein changes using dynamic light scattering Arch. Ophthalmol. 126 12 2008 1687 1693