@article{5b37e4e0eee241749bd8ca289b3d5087,
title = "On an inverse boundary problem arising in brain imaging",
abstract = "We consider the inverse problem of recovering both an unknown electric current and the surrounding electromagnetic parameters of a medium from boundary measurements. This inverse problem arises in brain imaging. We show that under generic conditions one can recover both the source and the electromagnetic parameters if these are piecewise constant and the source current is invariant in a fixed direction or a harmonic function, respectively.",
keywords = "Electroencephalography and magnetoencephalography, Identifiability and uniqueness, Inverse boundary problem, Maxwell system",
author = "Youjun Deng and Hongyu Liu and Gunther Uhlmann",
note = "Funding Information: The work of Y. Deng was supported by NSF grant of China No. 11601528, NSF grant of Hunan No. 2017JJ3432 and No. 2018JJ3622, Innovation-Driven Project of Central South University, No. 2018CX041, Mathematics and Interdisciplinary Sciences Project of Central South University. The work of H. Liu was supported by the FRG and startup grants from Hong Kong Baptist University, Hong Kong RGC General Research Funds, 12302415, 12302017 and 12301218. G. Uhlmann was partly supported by NSF and a Si Yuan professorship at IAS, HKUST. Funding Information: The work of Y. Deng was supported by NSF grant of China No. 11601528 , NSF grant of Hunan No. 2017JJ3432 and No. 2018JJ3622 , Innovation-Driven Project of Central South University , No. 2018CX041 , Mathematics and Interdisciplinary Sciences Project of Central South University . The work of H. Liu was supported by the FRG and startup grants from Hong Kong Baptist University , Hong Kong RGC General Research Funds, 12302415 , 12302017 and 12301218 . G. Uhlmann was partly supported by NSF and a Si Yuan professorship at IAS, HKUST . ",
year = "2019",
month = aug,
day = "5",
doi = "10.1016/j.jde.2019.03.019",
language = "English",
volume = "267",
pages = "2471--2502",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "4",
}