| Autor: |
Chow, Yat Tin, Han, Fuqun, Zou, Jun |
| Rok vydání: |
2020 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We propose a novel direct sampling method (DSM) for the effective and stable inversion of the Radon transform. The DSM is based on a generalization of the important almost orthogonality property in classical DSMs to fractional order Sobolev duality products and to a new family of probing functions. The fractional order duality product proves to be able to greatly enhance the robustness of the reconstructions in some practically important but severely ill-posed inverse problems associated with the Radon transform. We present a detailed analysis to better understand the performance of the new probing and index functions, which are crucial to stable and effective numerical reconstructions. The DSM can be computed in a very fast and highly parallel manner. Numerical experiments are carried out to compare the DSM with a popular existing method, and to illustrate the efficiency, stability, and accuracy of the DSM. |
| Databáze: |
arXiv |
| Externí odkaz: |
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