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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2405.04409 |
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| _version_ | 1866911970573156352 |
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| author | Lahtinen, Joonas |
| author_facet | Lahtinen, Joonas |
| contents | In electromagnetic source localization problems stemming from linearized Poisson-type equation, the aim is to locate the sources within a domain that produce given measurements on the boundary. In this type of problem, biasing of the solution is one of the main causes of mislocalization. A technique called standardization was developed to reduce biasing. However, the lack of a mathematical foundation for this method can cause difficulties in its application and confusion regarding the reliability of solutions. Here, we give a rigorous and generalized treatment for the technique using the Bayesian framework to shed light on the technique's abilities and limitations. In addition, we take a look at the noise robustness of the method, which is widely reported in numerical studies. The paper starts by giving a gentle introduction to the problem and its bias and works its way toward standardization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04409 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Bias and Its Reduction via Standardization in Discretized Electromagnetic Source Localization Problems Lahtinen, Joonas Optimization and Control 15A03, 15A04, 15A29, 15A42 In electromagnetic source localization problems stemming from linearized Poisson-type equation, the aim is to locate the sources within a domain that produce given measurements on the boundary. In this type of problem, biasing of the solution is one of the main causes of mislocalization. A technique called standardization was developed to reduce biasing. However, the lack of a mathematical foundation for this method can cause difficulties in its application and confusion regarding the reliability of solutions. Here, we give a rigorous and generalized treatment for the technique using the Bayesian framework to shed light on the technique's abilities and limitations. In addition, we take a look at the noise robustness of the method, which is widely reported in numerical studies. The paper starts by giving a gentle introduction to the problem and its bias and works its way toward standardization. |
| title | On Bias and Its Reduction via Standardization in Discretized Electromagnetic Source Localization Problems |
| topic | Optimization and Control 15A03, 15A04, 15A29, 15A42 |
| url | https://arxiv.org/abs/2405.04409 |