Inversion of tikhonov and truncated singular value decomposition regularization for noisy dynamic light scattering data

Ya-jing WANG; Xi YUAN; Jin SHEN; Zhen-hai DOU; Xian-ming SUN

doi:10.3788/OPE.20182609.2267

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Inversion of tikhonov and truncated singular value decomposition regularization for noisy dynamic light scattering data

更新时间：2020-08-13

- Inversion of tikhonov and truncated singular value decomposition regularization for noisy dynamic light scattering data
- Optics and Precision Engineering Vol. 26, Issue 9, Pages: 2269-2279(2018)
- 作者机构：
  
  山东理工大学电气与电子工程学院, 山东淄博 255049
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20182609.2267
  CLC： O433.4
- Received：28 May 2018，
  
  Accepted：02 July 2018，
  
  Published：25 September 2018
- 稿件说明：
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Ya-jing WANG, Xi YUAN, Jin SHEN, et al. Inversion of tikhonov and truncated singular value decomposition regularization for noisy dynamic light scattering data[J]. Optics and precision engineering, 2018, 26(9): 2269-2279.
DOI：

Ya-jing WANG, Xi YUAN, Jin SHEN, et al. Inversion of tikhonov and truncated singular value decomposition regularization for noisy dynamic light scattering data[J]. Optics and precision engineering, 2018, 26(9): 2269-2279. DOI： 10.3788/OPE.20182609.2267.

摘要

Tikhonov与截断奇异（TSVD）正则化是动态光散射数据反演中的两种重要方法，不同的正则化方法会对噪声DLS数据测量结果产生不同的影响。分别采用二阶差分矩阵的Tikhonov与TSVD方法，在6种噪声水平下，对宽窄不同的单峰与双峰分布颗粒进行了反演研究。结果表明：Tikhonov具有较好的光滑性；对于单峰分布颗粒，TSVD峰值误差更小、对于窄分布以及强噪声宽分布颗粒系反演，其抗噪性能更强、反演误差更小；对于双峰分布颗粒，Tikhonov具有较小的反演误差、较强的双峰分辨能力与抗噪声能力；对于窄分布颗粒的反演，一般TSVD峰值误差更小。在同样噪声情况下，Tikhonov与TSVD的双峰分辨力与颗粒的粒径峰值比有关。Tikhonov双峰分辨力较强，能够分辨出峰值比较低的颗粒。对实测200 nm单峰颗粒进行反演，Tikhonov、TSVD的反演峰值误差分别为3%和1.85%，TSVD峰值位置更准确，能够验证模拟数据的结论。

Abstract

Tikhonov and truncated singular value decomposition regularization (TSVD) are two important methods in the dynamic light-scattering (DLS) data inversion. Different regularization methods will have different effects on the results of noisy measurement data. By using the Tikhonov of second-order differential matrix and TSVD method

the unimodal and bimodal distribution particles with different widths were retrieved under six kinds of noise levels. The results show that Tikhonov had better smoothness

the peak value error of TSVD is smaller for unimodal distribution particles

anti-interference ability is stronger

and the inversion relative error is smaller for a narrow distribution and the strong noise wide distribution particle system. For bimodal distribution particles

Tikhonov has smaller inversion error and higher bimodal peak resolution and anti-interference ability. For the inversion of narrow distributed particles

the peak value error of TSVD is generally smaller. Under the same noise condition

the bimodal peak resolution of Tikhonov and TSVD is related to the peak value ratio of the particle size. Tikhonov has a high bimodal peak resolution

and it can distinguish particles with lower peak value ratio. The measured data are retrieved for unimodal distribution particles of size 200 nm. The inversion peak errors of Tikhonov and TSVD are 3% and 1.85%

respectively. The results verify the conclusion of the simulated data.

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Inversion of dynamic light scattering combining Tikhonov regularization with multi-grid technique

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Wang Ya-jing

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College of Electrical and Electronic Engineering, Shandong University of Technology, Zibo 255049, China

College of Optics and Electronic Information Engineering, Shanghai University of Science and Technology, Shanghai 200093, China

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