多参数正则化的动态光散射测量数据反演
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摘要
针对多分散颗粒体系反演中防止出现虚假峰和避免真实峰值信息丢失之间存在的矛盾,在正则化反演中,通过对小奇异值的截断处理和利用调节因子构造正则参数函数,在抑制小奇异值对噪声放大作用的同时,避免了单一正则参数导致的过正则化或欠正则化问题。由于过正则化会引起峰值信息的丢失,而欠正则化则会导致虚假峰、峰值分瓣或毛刺,因此,这一处理显著提高了反演方法的抗噪性能和多峰识别能力。模拟与实测动态光散射数据的反演结果表明,多参数正则化方法在准确给出粒度峰值的同时,有效地消除了虚假峰、峰值分瓣和毛刺等现象,实现了多峰颗粒体系的准确测量。
To prevent appearance of false peaks and avoid the loss of true peak information in the inversion of multi dispersive particles, in the regularized inversion, regular parameter functions are constructed by truncating the small singular values and using regulation factors. It not only eliminates noise amplification by small singular values, but also avoids over regularization or under regularization caused by improper single regularization parameters. Over regularization can cause the loss of peak information in the inversion results, and the under regularization will lead to false peaks, peak petals or burrs. Therefore, the multi parameter regularization significantly improves the noise-resistibility and multi peak recognition ability of the inversion method. The inversion results of the simulated and measured dynamic light scattering data show that the multi parameter regularization method can effectively eliminate the false peaks, peak petals and burrs, and realize the accurate measurement of the multi peak particle system.
To prevent appearance of false peaks and avoid the loss of true peak information in the inversion of multi dispersive particles, in the regularized inversion, regular parameter functions are constructed by truncating the small singular values and using regulation factors. It not only eliminates noise amplification by small singular values, but also avoids over regularization or under regularization caused by improper single regularization parameters. Over regularization can cause the loss of peak information in the inversion results, and the under regularization will lead to false peaks, peak petals or burrs. Therefore, the multi parameter regularization significantly improves the noise-resistibility and multi peak recognition ability of the inversion method. The inversion results of the simulated and measured dynamic light scattering data show that the multi parameter regularization method can effectively eliminate the false peaks, peak petals and burrs, and realize the accurate measurement of the multi peak particle system.
引文
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[15] 林承军, 沈建琪, 王天恩. 前向散射颗粒粒径测量中的多参数正则化算法[J]. 中国激光, 2016(11):165-173.
[16] 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.
[17] Gazzola S, Reichel L. A new framework for multi-parameter regularization [J]. Bit Numerical Mathematics, 2016, 56(3):919-949.
[18] 刘伟, 王雅静, 陈文钢, 等. 正则矩阵对双峰分布动态光散射数据反演的影响[J].中国激光, 2015, 42(9):252-261.
[19] Yu A B, Standish N. A study of particle size distribution [J]. Powder Technology,1990, 62(2):101-118.
[2] Kato H, Nakamura A, Ouchi N, et al. Determination of bimodal size distribution using dynamic light scattering methods in the submicrometer size range[J]. Materials Express, 2016, 6(2):175-182.
[3] 王志永, 蔡小舒, 徐呈泽,等. 动态光散射图像法测量纳米颗粒粒度研究[J]. 光学学报, 2014, 34(1):274-279.
[4] Xu M, Shen J, Thomas J C, et al. Information-weighted constrained regularization for particle size distribution recovery in multiangle dynamic light scattering[J]. Optics Express, 2018, 26(1):15-31.
[5] Stetefeld J, Mckenna S A, Patel T R. Dynamic light scattering: a practical guide and applications in biomedical sciences[J]. Biophysical Reviews, 2016, 8(4):1-19.
[6] Zhu X, Shen J, Song L. Accurate retrieval of bimodal particle size distribution in dynamic light scattering[J]. IEEE Photonics Technology Letters, 2015, 28(3):311-314.
[7] 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.
[8] Finsy R, Jaeger N D, Sneyers 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(2): 125-137.
[9] 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.
[10] Rasteiro M G, Lemos C, Vasquez A. Nanoparticle characterization by PCS: The analysis of bimodal distributions[J]. Particulate Science & Technology, 2008, 26(5):413-437.
[11] 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.
[12] Finsy R, Groen P D, Deriemaeker L, et al. Data analysis of multi-angle photon correlation measurements without and with prior knowledge[J]. Particle & Particle Systems Characterization, 1992, 9(4):237-251.
[13] Boualem A,Jabloun M,Ravier P,et al.An improved Bayesian inversion method for the estimation of multimodal particle size distributions using multiangle Dynamic Light Scattering measurements[C]//Statistical Signal Processing[s.l.]: IEEE, 2015: 360-363.
[14] Nyeo S L, Ansari R R. Data inversion for dynamic light scattering using Fisher information[J]. Laser Physics, 2015, 25(7): 075703.
[15] 林承军, 沈建琪, 王天恩. 前向散射颗粒粒径测量中的多参数正则化算法[J]. 中国激光, 2016(11):165-173.
[16] 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.
[17] Gazzola S, Reichel L. A new framework for multi-parameter regularization [J]. Bit Numerical Mathematics, 2016, 56(3):919-949.
[18] 刘伟, 王雅静, 陈文钢, 等. 正则矩阵对双峰分布动态光散射数据反演的影响[J].中国激光, 2015, 42(9):252-261.
[19] Yu A B, Standish N. A study of particle size distribution [J]. Powder Technology,1990, 62(2):101-118.
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