A novel iterative integration regularization method for ill-posed inverse problems

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Publicado en:Engineering with Computers vol. 37, no. 3 (Jul 2021), p. 1921
Autor principal: Huang, Ce
Otros Autores: Wang, Li, Fu Minghui, Zhong-Rong, Lu, Chen Yanmao
Publicado:
Springer Nature B.V.
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024 7 |a 10.1007/s00366-019-00920-z  |2 doi 
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045 2 |b d20210701  |b d20210731 
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100 1 |a Huang, Ce  |u Sun Yat-sen University, Department of Applied Mechanics and Engineering, Guangzhou, People’s Republic of China (GRID:grid.12981.33) (ISNI:0000 0001 2360 039X) 
245 1 |a A novel iterative integration regularization method for ill-posed inverse problems 
260 |b Springer Nature B.V.  |c Jul 2021 
513 |a Journal Article 
520 3 |a This paper proposes a new iterative integration regularization method for robust solution of ill-posed inverse problems. The proposed method is motivated from the fact that inversion of a positive definite matrix can be expressed in an integral form. Then, the development of the proposed method is mainly twofold. Firstly, two ways—including the linear iteration and the exponential (2j<inline-graphic xlink:href="366_2019_920_Article_IEq1.gif" />) iteration—are invoked to compute the integral, of which the exponential iteration is often preferred due to its fast convergence. Secondly, after stability analysis, the proposed method is shown able to filter out the undesired effect of relatively small singular values, while preserving the desired terms of relatively large singular values, i.e., the proposed method has the guaranteed regularization effect. Numerical examples on three typical ill-posed problems are conducted with detailed comparison to some usual direct and iterative regularization methods. Final results have highlighted the proposed method: (a) due to the iterative nature, the proposed method often turns out to be more efficient than the conventional direct regularization methods including the Tikhonov regularization and the truncated singular value decomposition (TSVD), (b) the proposed method converges much faster than the Landweber method and (c) the regularization effect is guaranteed in the proposed method, while may not be in the conjugate gradient method for least squares problem (CGLS). 
653 |a Regularization 
653 |a Singular value decomposition 
653 |a Convergence 
653 |a Mathematical analysis 
653 |a Matrices (mathematics) 
653 |a Inverse problems 
653 |a Iterative methods 
653 |a Ill posed problems 
653 |a Least squares method 
653 |a Regularization methods 
653 |a Conjugate gradient method 
653 |a Stability analysis 
653 |a Robustness (mathematics) 
653 |a Integrals 
700 1 |a Wang, Li  |u Sun Yat-sen University, Department of Applied Mechanics and Engineering, Guangzhou, People’s Republic of China (GRID:grid.12981.33) (ISNI:0000 0001 2360 039X) 
700 1 |a Fu Minghui  |u Sun Yat-sen University, Department of Applied Mechanics and Engineering, Guangzhou, People’s Republic of China (GRID:grid.12981.33) (ISNI:0000 0001 2360 039X) 
700 1 |a Zhong-Rong, Lu  |u Sun Yat-sen University, Department of Applied Mechanics and Engineering, Guangzhou, People’s Republic of China (GRID:grid.12981.33) (ISNI:0000 0001 2360 039X) 
700 1 |a Chen Yanmao  |u Sun Yat-sen University, Department of Applied Mechanics and Engineering, Guangzhou, People’s Republic of China (GRID:grid.12981.33) (ISNI:0000 0001 2360 039X) 
773 0 |t Engineering with Computers  |g vol. 37, no. 3 (Jul 2021), p. 1921 
786 0 |d ProQuest  |t Advanced Technologies & Aerospace Database 
856 4 1 |3 Citation/Abstract  |u https://www.proquest.com/docview/2548895250/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch 
856 4 0 |3 Full Text - PDF  |u https://www.proquest.com/docview/2548895250/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch