EARLY CATARACT DETECTION BY DYNAMIC LIGHT SCATTERING WITH SPARSE BAYESIAN LEARNING

SU-LONG NYEO; RAFAT R. ANSARI

[1] R. R. Ansari, M. B. III. Datiles, “Use of dynamic light scattering and Scheimpflug imaging for the early detection of cataracts,” Diabetes Technology & Therapeutics 1, 159–168 (1999).

[2] R. R. Ansari, “Ocular static and dynamic light scattering: A noninvasive diagnostic tool for eye research and clinical practice,” J. Biomed. Opt. 9, 22–37 (2004).

[3] M. Van Laethem, B. Babusiaux, A. Neetens, J. Clauwaert, “Photon correlation spectroscopy of light scattered by eye lenses in in vivo conditions,” Biophysical J. 59, 433–444 (1991).

[4] M. B. III. Datiles, R. R. Ansari, K. I. Suh, S. Vitale, G. F. Reed, J. S. Jr. Zigler, F. L. III. Ferris, “Clinical detection of precataractous lens protein changes using dynamic light scattering,” Arch. Ophthalmol. 126, 1687–1693 (2008).

[5] D. A. Ross, N. Dimas, “Particle sizing by dynamic light scattering: Noise and distortion in correlation data,” Part. & Part. Syst. Charact. 10, 62–69 (1993).

[6] H. Ruf, E. Grell, E. H. K. Stelzer, “Size distribution of submicron particles by dynamic light scattering measurements: Analyses considering normalization errors,” Eur. Biophys. J. 21, 21–28 (1992).

[7] D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: The method of cumulants,” J. Chem. Phys. 57, 4814– 4820 (1972).

[8] J. G. McWhirter, E. R. Pike, “On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind,” J. Phys. A 11, 1729–1745 (1978).

[9] N. Ostrowsky, D. Sornette, P. Parker, E. R. Pike, “Exponential sampling method for light scattering polydispersity analysis,” J. Mod. Optics 28, 1059– 1070 (1981).

[10] S. W. Provencher, “CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27, 229–242 (1982).

[11] A. K. Livesey, P. Licinio, M. Delaye, “Maximum entropy analysis of quasielastic light scattering from colloidal dispersions,” J. Chem. Phys. 84, 5102– 5107 (1986).

[12] S.-L. Nyeo, B. Chu, “Maximum-entropy analysis of photon correlation spectroscopy data,” Macromolecules 22, 3998–4009 (1989).

[13] C.-D. Sun, Z. Wang, G. Wu, B. Chu, “An improvement on maximum entropy analysis of photon correlation spectroscopy data,” Macromolecules 25, 1114–1120 (1992).

[14] R. K. Bryan, “Maximum entropy analysis of oversampled data problems,” Eur. Biophys. J. 18, 165– 174 (1990).

[15] J. Langowski, R. Bryan, “Maximum entropy analysis of photon correlation spectroscopy data using a Bayesian estimate for the regularization parameter,” Macromolecules 24, 6346–6348 (1991).

[16] M. E. Tipping, “Sparse Bayesian learning and the relevance vector machine,” J. Mach. Learn. Res. 1, 211–244 (2001).

[17] V. N. Vapnik, Statistical Learning Theory, Wiley, New York (1998).

[18] B. Chu, Laser Light Scattering: Basic Principles and Practice, 2nd Edition, Academic Press Inc., Boston (1991).

[19] R. Xu, Particle Characterization: Light Scattering Methods, Springer-Verlag, Netherland (2000).

[20] D. P. Wipf, B. D. Rao, “Sparse Bayesian learning for basis selection,” IEEE Trans. Signal Process. 52, 2153–2164 (2004).

[21] S. K. Majumder, N. Ghosh, P. K. Gupta, “Relevance vector machine for optical diagnosis of cancer,” Lasers Surg. Med. 36, 323–333 (2005).

[22] J. T. Flake, Application of the Relevance Vector Machine to Canal Flow Prediction in the Sevier River Basin, MSc. Thesis, Utah State University, Logan, Utah (2007).

[23] J.-Y. Peng, J. A. D. Aston, R. N. Gunn, C.-Y. Liou, J. Ashburner, “Dynamic positron emission tomography data-driven analysis using sparse Bayesian learning,” IEEE Trans. Med. Imag. 27, 1356–1369 (2008).

[24] C. L. Lawson, R. J. Hanson, Solving Least Squares Problems, Prentice-Hall Inc., Englewood Cliffs, (1974); also available as Classics in Applied Mathematics, Vol. 15, SIAM, Philadelphia, PA (1995); and reprinted with a detailed “new developments” appendix in 1996 by SIAM.

[25] D. MacKay, “The evidence framework applied to classification networks,” Neural Computation, 4, 720–736 (1992).

[26] P. J. McCarthy, “Direct analytic model of the Lcurve for Tikhonov regularization parameter selection,” Inverse Problems 19, 643–663 (2003).

[27] P. C. Hansen, “Regularization tools version 4.0 for Matlab 7.3,” Numerical Algorithms 46, 189–194 (2007).

[28] L. Reichel, H. Sadok, “A new L-curve for ill-posed problems,” J. Comput. Appl. Math. 219, 493–508 (2008).

[29] G. Rodriguez, D. Theis, “An algorithm for estimating the optimal regularization parameter by the L-curve,” Rendiconti di Matematica, Serie VII 25, 69–84 (2005).

[30] V. A. Morozov, “On the solution of functional equations by the method of regularization,” Soviet Math. Doklady 7, 414–417 (1966).

[31] O. Scherzer, “The use of Morozov’s discrepancy principle for Tikhonov regularization for solving nonlinear ill-posed problems,” Computing 51, 45–60 (1993). J. Innov. Opt. Health Sci. 2009.02:303-313. Downloaded from www.worldscientific.com by