Multi-penalty Regularization Inversion in Dynamic Light Scattering

XIU Wen-zheng; SHEN Jin; XU Min; ZHU Xin-jun; GAO Ming-liang; LIU Wei; WANG Ya-jing

doi:10.3788/gzxb20184701.0129001

[1] KOPPEL D E. Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants［J］. Journal of Chemical Physics, 1972, 57(11): 4814-4820.

[2] FINSY R, JAEGER I N D, SNEYERS I R, et al. Particle sizing by photon correlation spectroscopy. Part iii: Mono and bimodal distributions and data analysis［J］. Particle & Particle Systems Characterization, 1992, 9(1-4): 125-137.

[3] PROVENCHER S W. CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations［J］. Computer Physics Communications, 1982, 27(3): 229-242.

[4] OSTROWSKY N, SORNETTE D, PARKER P, et al. Exponential sampling method for light scattering polydispersity analysis［J］. Journal of Modern Optics, 1981, 28(8): 1059-1070.

[5] ZHU X J, SHEN J, LIU W, et al. Nonnegative least-squares truncated singular value decomposition to particle size distribution inversion from dynamic light scattering data［J］. Applied Optics, 2010, 49(34): 6591-6596.

[6] MAO S, SHEN J, ZHU X J, et al. Modified regularized solution of truncated singular value decomposition with chahine algorithm in dynamic light scattering (DLS) measurements［J］. Lasers in Engineering, 2013, 26(26): 45-47.

[7] MORRISON I D, GRABOWSKI E F, HERB C A. Improved techniques for particle size determination by quasi-elastic light scattering［J］. Langmuir, 1985, 1(4): 496-501.

[8] CUMMINS P G, STAPLES E J. Particle size distributions determined by a "multiangle" analysis of photon correlation spectroscopy data［J］. Langmuir, 1987, 3(6): 1109-1113.

[9] BRYANT G, THOMAS J C. Improved particle size distribution measurements using multiangle dynamic light scattering［J］. Langmuir, 1995, 11(7): 2480-2485.

[10] RASTEIRO M G, LEMOS C C, VASQUEZ A. Nanoparticle characterization by PCS: The analysis of bimodal distributions［J］. Particulate Science & Technology, 2008, 26(5): 413-437.

[11] YANKOVSKII G M, KUZNETSOV D V, KONDAKOV S E, et al. Solution of inverse problem of light beating spectroscopy using Tikhonov method of regularization for analyzing polydisperse suspensions of nanoparticles［J］. Moscow University Chemistry Bulletin, 2013, 68(5): 238-245.

[12] WANG Y J, SHEN J, LIU W, et al. Non-negative constraint research of Tikhonov regularization inversion for dynamic light scattering［J］. Laser Physics, 2013, 23(8): 085701-085707.

[13] HASSAN P A, RANA S, VERMA G. Making sense ofBrownian motion: Colloid characterization by dynamic light scattering［J］. Langmuir the Acs Journal of Surfaces & Colloids, 2014, 31(1): 3-12.

[14] VEGA J R, GUGLIOTTA L M, GONZALEZ V D, et al. Latex particle size distribution by dynamic light scattering: novel data processing for multiangle measurements［J］. Journal of Colloid & Interface Science, 2003, 261(1): 74-81.

[15] HANSEN P C, O'LEARY D P. The use of the L-curve in the regularization of discrete ill-posed problems［J］. Siam Journal on Scientific Computing, 1993, 14(6): 1487-1503.

[16] GAZZOLA S, REICHEL L. A new framework for multi-parameter regularization［J］. Bit Numerical Mathematics, 2016, 56(3): 919-949.

[17] FORNASIER M, NAUMOVA V, PEREVERZYEV S V. Parameter choice strategies for multipenalty regularization［J］. Siam Journal on Numerical Analysis, 2014, 52(4): 1770-1794.

[18] BELGE M, KILMER M E, MILLER E L. Efficient determination of multiple regularization parameters in a generalized L-curve framework［J］. Inverse Problems, 2001, 18(4): 1161-1183.

[19] NAUMOVA V, PETER S. Minimization of multi-penalty functionals by alternating iterative thresholding and optimal parameter choices［J］. Inverse Problems, 2014, 30(12): 125003-125036.

[20] NAUMOVA V, PEREVERZYEV S V. Multi-penalty regularization with a component-wise penalization［J］. Inverse Problems, 2013, 29(7): 075002-075018.

[21] XIAO Ying-ying, SHEN Jin, WANG Ya-jing, et al. Influence of initial model on regularized inversion of noisy dynamic light scattering data［J］. High Power Laser and Particle Beams, 2014, 26(12): 260-267.

[22] WANG Ze-wen. Multi-parameter Tikhonov regularization and model function approach to the damped Morozov principle for choosing regularization parameters［J］. Journal of Computational & Applied Mathematics, 2012, 236(7): 1815-1832.

[23] THOMAS J C. The determination of log normal particle size distributions by dynamic light scattering［J］. Journal of Colloid & Interface Science, 1987, 117(1): 187-192.