Reconstructions for some coupled-physics inverse problems

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• 作者：Guillaume Bal^a ; ^{gb2030@columbia.edu} ; Gunther Uhlmann^b ; ^c ; ^{gunther@math.washington.edu}
• 关键词：Inverse problems ; Coupled-physics inverse problems ; Hybrid inverse problems ; Elliptic equations ; Anisotropic reconstructions
• 刊名：Applied Mathematics Letters
• 出版年：2012
• 期刊代码：5_08939659
• 类别：mt
• 出版时间：July, 2012
• 卷：25
• 期：7
• 页码：1030-1033
• 文件大小：216 K

摘要

This letter announces and summarizes results obtained in Bal and Uhlmann (2011) and considers several natural extensions. The aforementioned paper proposes a procedure for reconstructing coefficients in a second-order, scalar, elliptic equation from knowledge of a sufficiently large number of its solutions. We present this derivation and extend it to show which parameters may or may not be reconstructed for several hybrid (also called coupled-physics) imaging modalities including photo-acoustic tomography, thermo-acoustic tomography, transient elastography, and magnetic resonance elastography. Stability estimates are also proposed.