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Volumn 141, Issue 10, 2013, Pages 3431-3446

Resolution and stability analysis in full-aperture, linearized conductivity and wave imaging

Author keywords

Inverse conductivity problem; Resolution; Stability; Wave imaging

Indexed keywords


EID: 84880720585     PISSN: 00029939     EISSN: 10886826     Source Type: Journal    
DOI: 10.1090/S0002-9939-2013-11590-X     Document Type: Article
Times cited : (22)

References (27)
  • 4
    • 77950653003 scopus 로고    scopus 로고
    • Layer Potential Techniques in Spectral Analysis
    • Amer. Math. Soc., Providence, RI, MR2488135 (2010j:47062)
    • H. Ammari, H. Kang, and H. Lee, Layer Potential Techniques in Spectral Analysis, Mathematical Surveys and Monographs, Vol. 153, Amer. Math. Soc., Providence, RI, 2009. MR2488135 (2010j:47062)
    • (2009) Mathematical Surveys and Monographs , vol.153
    • Ammari, H.1    Kang, H.2    Lee, H.3
  • 5
    • 77950915517 scopus 로고    scopus 로고
    • Conductivity interface problems. Part I: Small perturbations of an interface
    • MR2584606
    • H. Ammari, H. Kang, M. Lim, and H. Zribi, Conductivity interface problems. Part I: Small perturbations of an interface, Trans. Amer. Math. Soc., 362 (2010), 2435-2449. MR2584606
    • (2010) Trans. Amer. Math. Soc. , vol.362 , pp. 2435-2449
    • Ammari, H.1    Kang, H.2    Lim, M.3    Zribi, H.4
  • 6
    • 0034216316 scopus 로고    scopus 로고
    • Regularity and stability for the scattering map of a linearized inverse medium problem
    • MR1766937 (2001f:35423)
    • G. Bao, Y. Chen, and F. Ma, Regularity and stability for the scattering map of a linearized inverse medium problem, J. Math. Anal. Appl., 247 (2000), 255-271. MR1766937 (2001f:35423)
    • (2000) J. Math. Anal. Appl. , vol.247 , pp. 255-271
    • Bao, G.1    Chen, Y.2    Ma, F.3
  • 7
    • 67649356809 scopus 로고    scopus 로고
    • Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of thin inhomogeneities, in Inverse problems: Theory and applications
    • Amer. Math. Soc., Providence, RI, MR2032006 (2005a:35263)
    • E. Beretta and E. Francini, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of thin inhomogeneities, in Inverse problems: theory and applications, Contemp. Math., 333, Amer. Math. Soc., Providence, RI, 2003. MR2032006 (2005a:35263)
    • (2003) Contemp. Math. , vol.333
    • Beretta, E.1    Francini, E.2
  • 8
    • 0009560034 scopus 로고    scopus 로고
    • Resolution and super-resolution in inverse diffraction, in Inverse Problems of Wave Propagation and Diffraction
    • Springer, Berlin, MR1601171 (98j:65073)
    • M. Bertero, P. Boccacci, and M. Piana, Resolution and super-resolution in inverse diffraction, in Inverse Problems of Wave Propagation and Diffraction, Lecture Notes in Physics, Vol. 486, 1-17, Springer, Berlin, 1997. MR1601171 (98j:65073)
    • (1997) Lecture Notes in Physics , vol.486 , pp. 1-17
    • Bertero, M.1    Boccacci, P.2    Piana, M.3
  • 9
    • 0036904346 scopus 로고    scopus 로고
    • Electrical impedance tomography
    • MR1955896
    • L. Borcea, Electrical impedance tomography, Inverse Problems 18 (2002), R99-R136. MR1955896
    • (2002) Inverse Problems , vol.18
    • Borcea, L.1
  • 10
    • 85009211564 scopus 로고    scopus 로고
    • Edge illumination and imaging of extended reflectors
    • MR2475826 (2010a:15028)
    • L. Borcea, G. Papanicolaou, and F. G. Vasquez, Edge illumination and imaging of extended reflectors, SIAM J. Imaging Sci., 1 (2008), 75-114. MR2475826 (2010a:15028)
    • (2008) SIAM J. Imaging Sci. , vol.1 , pp. 75-114
    • Borcea, L.1    Papanicolaou, G.2    Vasquez, F.G.3
  • 11
  • 12
    • 0002912660 scopus 로고
    • Estimates on resolution and stabilization for the linearized inverse conductivity problem
    • MR1153128 (92m:35269)
    • D. C. Dobson, Estimates on resolution and stabilization for the linearized inverse conductivity problem, Inverse Problems, 8 (1992), 71-81. MR1153128 (92m:35269)
    • (1992) Inverse Problems , vol.8 , pp. 71-81
    • Dobson, D.C.1
  • 13
    • 0028728116 scopus 로고
    • Resolution and stability analysis of an inverse problem in electrical impedance tomography: Dependence on the input current patterns
    • MR1301272 (95g:35212)
    • D. C. Dobson and F. Santosa, Resolution and stability analysis of an inverse problem in electrical impedance tomography: dependence on the input current patterns, SIAM J. Appl. Math., 54 (1994), 1542-1560. MR1301272 (95g:35212)
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1542-1560
    • Dobson, D.C.1    Santosa, F.2
  • 14
    • 33746281672 scopus 로고    scopus 로고
    • Resolution and denoising in near-field imaging
    • MR2249472 (2007b:76110)
    • G. Derveaux, G. Papanicolaou, and C. Tsogka, Resolution and denoising in near-field imaging, Inverse Problems, 22 (2006), 1437-1456. MR2249472 (2007b:76110)
    • (2006) Inverse Problems , vol.22 , pp. 1437-1456
    • Derveaux, G.1    Papanicolaou, G.2    Tsogka, C.3
  • 17
    • 77956066305 scopus 로고    scopus 로고
    • Exact shape-reconstruction by one-step linearization in electrical impedance tomography
    • MR2679585 (2011h:35316)
    • B. Harrach and J. K. Seo, Exact shape-reconstruction by one-step linearization in electrical impedance tomography, SIAM J. Math. Anal., 42 (2010), 1505-1518. MR2679585 (2011h:35316)
    • (2010) SIAM J. Math. Anal. , vol.42 , pp. 1505-1518
    • Harrach, B.1    Seo, J.K.2
  • 18
    • 33746279922 scopus 로고    scopus 로고
    • A direct imaging algorithm for extended targets
    • MR2249458 (2007b:78009)
    • S. Hou, K. Sølna, and H. Zhao, A direct imaging algorithm for extended targets, Inverse Problems, 22 (2006), 1151-1178. MR2249458 (2007b:78009)
    • (2006) Inverse Problems , vol.22 , pp. 1151-1178
    • Hou, S.1    Sølna, K.2    Zhao, H.3
  • 19
    • 4344637225 scopus 로고    scopus 로고
    • Imaging of location and geometry for extended targets using the response matrix
    • MR2081006 (2005k:78016)
    • S. Hou, K. Sølna, and H. Zhao, Imaging of location and geometry for extended targets using the response matrix, J. Comput. Phys., 199 (2004), 317-338. MR2081006 (2005k:78016)
    • (2004) J. Comput. Phys. , vol.199 , pp. 317-338
    • Hou, S.1    Sølna, K.2    Zhao, H.3
  • 20
    • 84966233626 scopus 로고
    • Comment on A.-P. Calderón paper: "On an inverse boundary value problem"
    • MR962208 (90f:35201)
    • D. Isaacson and E. L. Isaacson, Comment on A.-P. Calderón paper: "On an inverse boundary value problem", Math. Comp., 52 (1989), 553-559. MR962208 (90f:35201)
    • (1989) Math. Comp. , vol.52 , pp. 553-559
    • Isaacson, D.1    Isaacson, E.L.2
  • 21
    • 77951990301 scopus 로고    scopus 로고
    • Increased stability in the Cauchy problem for some elliptic equations, in Instability in Models Connected with Fluid Flows
    • I, C. Bardos and A. Fursikov, eds., Springer, MR2459261 (2009g:35038)
    • V. Isakov, Increased stability in the Cauchy problem for some elliptic equations, in Instability in Models Connected with Fluid Flows. I, C. Bardos and A. Fursikov, eds., International Math. Series, Vol. 6, 339-362, Springer, 2008. MR2459261 (2009g:35038)
    • (2008) International Math. Series , vol.6 , pp. 339-362
    • Isakov, V.1
  • 23
    • 0035473445 scopus 로고    scopus 로고
    • Exponential instability in an inverse problem for the Schrödinger equation
    • MR1862200 (2002h:35339)
    • N. Mandache, Exponential instability in an inverse problem for the Schrödinger equation, Inverse Problems, 17 (2001), 1435-1444. MR1862200 (2002h:35339)
    • (2001) Inverse Problems , vol.17 , pp. 1435-1444
    • Mandache, N.1
  • 24
    • 70350676977 scopus 로고    scopus 로고
    • Depth dependent stability estimates in electrical impedance tomography
    • MR2519853 (2010g:65195)
    • S. Nagayasu, G. Uhlmann, and J.-N. Wang, Depth dependent stability estimates in electrical impedance tomography, Inverse Problems, 25 (2009), 075001. MR2519853 (2010g:65195)
    • (2009) Inverse Problems , vol.25 , pp. 075001
    • Nagayasu, S.1    Uhlmann, G.2    Wang, J.B.3
  • 25
    • 0020786063 scopus 로고
    • Some comments on Fourier analysis, uncertainty and modeling
    • MR710468 (84i:94016)
    • D. Slepian, Some comments on Fourier analysis, uncertainty and modeling, SIAM Review, 25 (1983), 379-393. MR710468 (84i:94016)
    • (1983) SIAM Review , vol.25 , pp. 379-393
    • Slepian, D.1
  • 26
    • 84966204035 scopus 로고
    • Asymptotic expansion of (λ cos θ)dθ
    • MR917830 (89g:41022)
    • R. Wong, Asymptotic expansion of (λ cos θ)dθ, Math. Comput., 50 (1988), 229-234. MR917830 (89g:41022)
    • (1988) Math. Comput. , vol.50 , pp. 229-234
    • Wong, R.1
  • 27
    • 3142751439 scopus 로고    scopus 로고
    • Analysis of the response matrix for an extended target
    • MR2068119 (2005a:74050)
    • H. Zhao, Analysis of the response matrix for an extended target, SIAM J. Appl. Math., 64 (2004), 725-745. MR2068119 (2005a:74050)
    • (2004) SIAM J. Appl. Math. , vol.64 , pp. 725-745
    • Zhao, H.1


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