Montalto, Carlos; Tamasan, Alexandru Stability in conductivity imaging from partial measurements of one interior current. (English) Zbl 1359.35229 Inverse Probl. Imaging 11, No. 2, 339-353 (2017). MSC: 35R30 35J65 65N21 PDF BibTeX XML Cite \textit{C. Montalto} and \textit{A. Tamasan}, Inverse Probl. Imaging 11, No. 2, 339--353 (2017; Zbl 1359.35229) Full Text: DOI arXiv
Nachman, Adrian; Tamasan, Alexandru; Veras, Johann A weighted minimum gradient problem with complete electrode model boundary conditions for conductivity imaging. (English) Zbl 1342.35454 SIAM J. Appl. Math. 76, No. 4, 1321-1343 (2016). MSC: 35R30 35J60 31A25 62P10 PDF BibTeX XML Cite \textit{A. Nachman} et al., SIAM J. Appl. Math. 76, No. 4, 1321--1343 (2016; Zbl 1342.35454) Full Text: DOI arXiv
Lee, Min Gi; Ko, Min-Su; Kim, Yong-Jung Virtual resistive network and conductivity reconstruction with Faraday’s law. (English) Zbl 1310.78010 Inverse Probl. 30, No. 12, Article ID 125009, 21 p. (2014). MSC: 78A46 78A30 78M20 PDF BibTeX XML Cite \textit{M. G. Lee} et al., Inverse Probl. 30, No. 12, Article ID 125009, 21 p. (2014; Zbl 1310.78010) Full Text: DOI
Chen, Qun; Liu, Jijun On the error estimate of the harmonic \(B_z\) algorithm in MREIT from noisy magnetic flux field. (English) Zbl 1298.35249 Chin. Ann. Math., Ser. B 35, No. 3, 319-336 (2014). MSC: 35R30 35J05 65N21 65N15 65N12 92C55 PDF BibTeX XML Cite \textit{Q. Chen} and \textit{J. Liu}, Chin. Ann. Math., Ser. B 35, No. 3, 319--336 (2014; Zbl 1298.35249) Full Text: DOI
Ersöz, Ali; Eyüboğlu, B. Murat Magnetic resonance current density imaging using one component of magnetic flux density. (English) Zbl 1327.92022 Inverse Probl. Sci. Eng. 21, No. 2, 184-196 (2013). MSC: 92C55 65N21 78A70 PDF BibTeX XML Cite \textit{A. Ersöz} and \textit{B. M. Eyüboğlu}, Inverse Probl. Sci. Eng. 21, No. 2, 184--196 (2013; Zbl 1327.92022) Full Text: DOI
Kwon, Oh-In; Park, Chunjae Newton method to recover the phase accumulated during MRI data acquisition. (English) Zbl 1264.92031 J. Appl. Math. 2012, Article ID 973781, 15 p. (2012). MSC: 92C55 94A08 PDF BibTeX XML Cite \textit{O.-I. Kwon} and \textit{C. Park}, J. Appl. Math. 2012, Article ID 973781, 15 p. (2012; Zbl 1264.92031) Full Text: DOI
Seo, Jin Keun; Jeon, Kiwan; Lee, Chang-Ock; Woo, Eung Je Non-iterative harmonic \(B_{z}\) algorithm in MREIT. (English) Zbl 1235.78028 Inverse Probl. 27, No. 8, Article ID 085003, 12 p. (2011). Reviewer: Witold Pedrycz (Edmonton) MSC: 78A55 PDF BibTeX XML Cite \textit{J. K. Seo} et al., Inverse Probl. 27, No. 8, Article ID 085003, 12 p. (2011; Zbl 1235.78028) Full Text: DOI
Jeon, Kiwan; Lee, Chang-Ock Denoising of \(B_z\) data for conductivity reconstruction in magnetic resonance electrical impedance tomography (MREIT). (English) Zbl 1239.78009 Ammari, Habib (ed.) et al., Mathematical and statistical methods for imaging. NIMS thematic workshop, Inha University, Incheon, Korea, August 10–13, 2010. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5289-7/pbk). Contemporary Mathematics 548, 85-100 (2011). MSC: 78A46 35R30 65M06 92C55 35P30 PDF BibTeX XML Cite \textit{K. Jeon} and \textit{C.-O. Lee}, Contemp. Math. 548, 85--100 (2011; Zbl 1239.78009)
Seo, Jin Keun; Woo, Eung Je Magnetic resonance electrical impedance tomography (MREIT). (English) Zbl 1210.35293 SIAM Rev. 53, No. 1, 40-68 (2011). MSC: 35R30 35J05 76Q05 78A70 78A46 35-02 78-02 PDF BibTeX XML Cite \textit{J. K. Seo} and \textit{E. J. Woo}, SIAM Rev. 53, No. 1, 40--68 (2011; Zbl 1210.35293) Full Text: DOI
Liu, Jijun; Seo, Jinkeun; Woo, Eungje A posteriori error estimate and convergence analysis for conductivity image reconstruction in MREIT. (English) Zbl 1210.35290 SIAM J. Appl. Math. 70, No. 8, 2883-2903 (2010). MSC: 35R30 35J05 76Q05 78A46 92C55 PDF BibTeX XML Cite \textit{J. Liu} et al., SIAM J. Appl. Math. 70, No. 8, 2883--2903 (2010; Zbl 1210.35290) Full Text: DOI
Chen, Qun; Huang, Biaozhang; Liu, Jijun An inverse problem for conductivity imaging with regularization. (Chinese. English summary) Zbl 1199.65321 Math. Numer. Sin. 31, No. 1, 51-64 (2009). MSC: 65M32 65M60 35Q60 78A25 92C55 65M15 PDF BibTeX XML Cite \textit{Q. Chen} et al., Math. Numer. Sin. 31, No. 1, 51--64 (2009; Zbl 1199.65321)
Lin, J. A uniqueness result and image reconstruction of the orthotropic conductivity in magnetic resonance electrical impedance tomography. (English) Zbl 1154.35469 J. Inverse Ill-Posed Probl. 16, No. 4, 381-396 (2008). MSC: 35R30 35Q80 65N21 92C55 PDF BibTeX XML Cite \textit{J. Lin}, J. Inverse Ill-Posed Probl. 16, No. 4, 381--396 (2008; Zbl 1154.35469) Full Text: DOI
Liu, J. J.; Pyo, H. C.; Seo, J. K.; Woo, E. J. Convergence properties and stability issues in MREIT algorithm. (English) Zbl 1110.35105 Ammari, Habib (ed.) et al., Inverse problems, multi-scale analysis and effective medium theory. Proceedings of the workshop on inverse problems, multi-scale analysis and homogenization, Seoul, Korea, June 22–24, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3968-3/pbk). Contemporary Mathematics 408, 201-218 (2006). MSC: 35R30 92C55 35J25 78A46 65N21 PDF BibTeX XML Cite \textit{J. J. Liu} et al., Contemp. Math. 408, 201--218 (2006; Zbl 1110.35105)
Kwon, Ohin; Park, Chunjae; Park, Eun-Jae; Seo, Jin Keun; Woo, Eung Je Electrical conductivity imaging using a variational method in \(B_z\)-based MREIT. (English) Zbl 1071.35126 Inverse Probl. 21, No. 3, 969-980 (2005). MSC: 35R30 35Q60 35J25 PDF BibTeX XML Cite \textit{O. Kwon} et al., Inverse Probl. 21, No. 3, 969--980 (2005; Zbl 1071.35126) Full Text: DOI
Lee, June-Yub A reconstruction formula and uniqueness of conductivity in MREIT using two internal current distributions. (English) Zbl 1086.35141 Inverse Probl. 20, No. 3, 847-858 (2004). MSC: 35R30 35Q60 78A35 PDF BibTeX XML Cite \textit{J.-Y. Lee}, Inverse Probl. 20, No. 3, 847--858 (2004; Zbl 1086.35141) Full Text: DOI
Kim, Sungwhan; Kwon, Ohin; Seo, Jin Keun; Yoon, Jeong-Rock On a nonlinear partial differential equation arising in magnetic resonance electrical impedance tomography. (English) Zbl 1055.35142 SIAM J. Math. Anal. 34, No. 3, 511-526 (2002). MSC: 35R30 31A25 35J60 92C55 PDF BibTeX XML Cite \textit{S. Kim} et al., SIAM J. Math. Anal. 34, No. 3, 511--526 (2002; Zbl 1055.35142) Full Text: DOI
Natterer, Frank Mathematical models for medical imaging. (English) Zbl 0938.92023 Börgers, Christoph (ed.) et al., Computational radiology and imaging. Therapy and diagnostics. Proceedings of a workshop, University of Minnesota, Minneapolis, MN, USA, March 17-21, 1997. New York, NY: Springer. IMA Vol. Math. Appl. 110, 17-32 (1999). MSC: 92C55 44A12 PDF BibTeX XML Cite \textit{F. Natterer}, IMA Vol. Math. Appl. 110, 17--32 (1999; Zbl 0938.92023)
Anger, G. On the efficiency of theory in natural sciences, technical sciences, and medicine – praxis cum theoria. (Zur Leistungsfähigkeit der Theorie in den Naturwissenschaften, der Technik und der Medizin – praxis cum theoria.) (German) Zbl 0894.92001 Mitt. Ges. Angew. Math. Mech. 20, No. 1, 19-36 (1997). Reviewer: G.Anger (Berlin) MSC: 92B05 92C05 92C50 PDF BibTeX XML Cite \textit{G. Anger}, Mitt. Ges. Angew. Math. Mech. 20, No. 1, 19--36 (1997; Zbl 0894.92001)
Anger, Gottfried On the efficiency of methods of natural sciences in medical diagnostics: praxis cum theoria. (Zur Leistungsfähigkeit naturwissenschaftlicher Methoden in der medizinischen Diagnostik: praxis cum theoria.) (German) Zbl 0894.92017 Arzt Krankenh. 12, 354-357 (1997). Reviewer: G.Anger (Berlin) MSC: 92C50 92B05 PDF BibTeX XML