Simulation research on magneto-acoustic concentration tomography of magnetic nanoparticles based on truncated singular value decomposition (TSVD)

2021 ◽  
Author(s):  
Xiaoheng Yan ◽  
Yu Hu ◽  
Sichen Guang ◽  
Weihua Chen
Keyword(s):  
Magnetic Nanoparticles ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Truncated Singular Value Decomposition ◽  
Simulation Research ◽  
Value Decomposition

scholarly journals A modified truncation singular value decomposition method for solving ill-posed problems

2018 ◽  
Vol 13 ◽  
pp. 174830181881360 ◽  
Author(s):  
Zhenyu Zhao ◽  
Riguang Lin ◽  
Zehong Meng ◽  
Guoqiang He ◽  
Lei You ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Decomposition Method ◽  
Singular Value ◽  
Numerical Results ◽  
New Method ◽  
Truncated Singular Value Decomposition ◽  
Singular Value Decomposition Method ◽  
Ill Posed ◽  
Value Decomposition

A modified truncated singular value decomposition method for solving ill-posed problems is presented in this paper, in which the solution has a slightly different form. Both theoretical and numerical results show that the limitations of the classical TSVD method have been overcome by the new method and very few additive computations are needed.

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

2018 ◽  
Vol 26 (9) ◽  
pp. 2269-2279
Author(s):  
王雅静 WANG Ya-jing ◽  
袁 曦 YUAN Xi ◽  
申 晋 SHEN Jin ◽  
窦震海 DOU Zhen-hai ◽  
孙贤明 SUN Xian-ming
Keyword(s):  
Light Scattering ◽  
Dynamic Light Scattering ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Scattering Data ◽  
Truncated Singular Value Decomposition ◽  
Value Decomposition ◽  
Dynamic Light Scattering Data

scholarly journals Toward efficacy of piecewise polynomial truncated singular value decomposition algorithm in moving force identification

2019 ◽  
Vol 22 (12) ◽  
pp. 2687-2698 ◽  
Author(s):  
Zhen Chen ◽  
Lifeng Qin ◽  
Shunbo Zhao ◽  
Tommy HT Chan ◽  
Andy Nguyen
Keyword(s):  
Singular Value Decomposition ◽  
Singular Values ◽  
Singular Value ◽  
Decomposition Algorithm ◽  
Identification Accuracy ◽  
Piecewise Polynomial ◽  
Truncated Singular Value Decomposition ◽  
Force Identification ◽  
Moving Force ◽  
Value Decomposition

This article introduces and evaluates the piecewise polynomial truncated singular value decomposition algorithm toward an effective use for moving force identification. Suffering from numerical non-uniqueness and noise disturbance, the moving force identification is known to be associated with ill-posedness. An important method for solving this problem is the truncated singular value decomposition algorithm, but the truncated small singular values removed by truncated singular value decomposition may contain some useful information. The piecewise polynomial truncated singular value decomposition algorithm extracts the useful responses from truncated small singular values and superposes it into the solution of truncated singular value decomposition, which can be useful in moving force identification. In this article, a comprehensive numerical simulation is set up to evaluate piecewise polynomial truncated singular value decomposition, and compare this technique against truncated singular value decomposition and singular value decomposition. Numerically simulated data are processed to validate the novel method, which show that regularization matrix [Formula: see text] and truncating point [Formula: see text] are the two most important governing factors affecting identification accuracy and ill-posedness immunity of piecewise polynomial truncated singular value decomposition.

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