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 |
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| Autor principal: | |
| Otros Autores: | , , , |
| Publicado: |
Springer Nature B.V.
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| Materias: | |
| Acceso en línea: | Citation/Abstract Full Text - PDF |
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| 024 | 7 | |a 10.1007/s00366-019-00920-z |2 doi | |
| 035 | |a 2548895250 | ||
| 045 | 2 | |b d20210701 |b d20210731 | |
| 084 | |a 137654 |2 nlm | ||
| 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 |