Elastic-net regularization for nonlinear electrical impedance tomography with a splitting approach

References

• Cheney M , Isaacson D , Newell JC . Electrical impedance tomography. SIAM Rev. 1999;41:85–101.
   Web of Science ®Google Scholar
• Borcea L . Electrical impedance tomography. Inverse Probl. 2002;18:99–136.
   Web of Science ®Google Scholar
• Holder DS , ed. Electrical impedance tomography: methods, history and applications[M]; Boca Raton: CRC Press; 2004.
   Google Scholar
• Vauhkonen M , Vadasz D , Karjalainen PA , et al . Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans Med Imaging. 1998;17(2):285–293.
   PubMed Web of Science ®Google Scholar
• Lukaschewitsch M , Maass P , Pidcock M . Tikhonov regularization for electrical impedance tomography on unbounded domains. Inverse Probl. 2003;19(3):585–610.
   Web of Science ®Google Scholar
• Strong D , Chan T . Edge-preserving and scale-dependent properties of total variation regularization. Inverse Probl. 2003;19(6):165–187.
   Web of Science ®Google Scholar
• Chung ET , Chan TF , Tai XC . Electrical impedance tomography using level set representation and total variational regularization. J Comput Phys. 2005;205(1):357–372.
   Web of Science ®Google Scholar
• Borsic A , Graham BM , Adler A , et al . Total variation regularization in electrical impedance tomography. Inverse Probl. 2007;99(99: A12):A12–A12.
   Google Scholar
• Borsic A , Graham BM , Adler A , et al . In vivo impedance imaging with total variation regularization. IEEE Trans Med Imaging. 2010;29(1):44–54.
   PubMed Web of Science ®Google Scholar
• Liu J , Ling L , Li G . A novel combined regularization algorithm of total variation and Tikhonov regularization for open electrical impedance tomography. Physiol Meas. 2013;34(7):823–838.
   PubMed Web of Science ®Google Scholar
• Daubechies I , Defrise M , De Mol C . An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl Math. 2004;57(11):1413–1457.
   Web of Science ®Google Scholar
• Loris I , Nolet G , Daubechies I , et al . Tomographic inversion using l1-norm regularization of wavelet coefficients. Geophys J Int. 2007;170(1):359–370.
   Web of Science ®Google Scholar
• Kutyniok G . Compressed sensing: theory and applications. Corr. 2012;52(4):1289–1306.
   Google Scholar
• Borsic A , Adler A . A primal-dual interior-point framework for using the l1 or l2-norm on the data and regularization terms of inverse problems. Inverse Probl. 2012;28(9):18–24.
   Web of Science ®Google Scholar
• Gehre M , Kluth T , Lipponen A , et al . Sparsity reconstruction in electrical impedance tomography: an experimental evaluation. J Comput Appl Math. 2012;236(8):2126–2136.
   Web of Science ®Google Scholar
• Gehre M , Kluth T , Sebu C , et al . Sparse 3D reconstructions in electrical impedance tomography using real data. Inverse Probl Sci Eng. 2014;22(1):31–44.
   Web of Science ®Google Scholar
• Jin B , Khan T , Maass P . A reconstruction algorithm for electrical impedance tomography based on sparsity regularization. Int J Numer Methods Eng. 2012;89(3):337–353.
   Web of Science ®Google Scholar
• Jin B , Lorenz D , Schiffler S . Elastic-net regularization: error estimates and active set methods. Inverse Probl. 2009;25(11):1595–1610.
   Web of Science ®Google Scholar
• Cheng KS , Isaacson D , Newell JC , et al . Electrode models for electric current computed tomography. IEEE Trans Biomed Eng. 1989;36(9):918–924.
   PubMed Web of Science ®Google Scholar
• Somersalo E , Cheney M , Isaacson D . Existence and uniqueness for electrode models for electric current computed tomography. SIAM J Appl Math. 1992;52(4):1023–1040.
   Web of Science ®Google Scholar
• Woo EJ , Hua P , Webster JG , et al . Finite-element method in electrical impedance tomography. Med Biol Eng Comput. 1994;32(5):530–536.
   PubMed Web of Science ®Google Scholar
• Vauhkonen M , Kaipio JP , Somersalo E , et al . Electrical impedance tomography with basis constraints. Inverse Probl. 1997;13(2):523–530.
   Web of Science ®Google Scholar
• Jin B , Maass P . An analysis of electrical impedance tomography with, applications to Tikhonov regularization. ESAIM Control Optim Calc Var. 2012;18(4):1027–1048.
   Web of Science ®Google Scholar
• Engl HW , Ramlau R . Regularization of inverse problems [J]. Problems[J]. 2015;43(2):347–366.
   Google Scholar
• Loris I . On the performance of algorithms for the minimization of l1-penalized functionals. Inverse Probl. 2009;25(25):35008–35023.
   Web of Science ®Google Scholar
• Goldstein T , Osher S . The split Bregman method for l1 regularized problems. SIAM J Imaging Sci. 2009;2(2):323–343.
   Web of Science ®Google Scholar
• Morozov VA . On the solution of functional equations by the method of regularization. Soviet Math Dokl. 1966;7(3):510–512.
   Google Scholar
• Vauhkonen M , Lionheart WR , Heikkinen LM , et al . A MATLAB package for the EIDORS project to reconstruct two-dimensional EIT images. Physiol Meas. 2001;22(1):107–111.
   PubMed Web of Science ®Google Scholar
• Wirgin A . The inverse crime. arXiv:math-ph/0401050; 2004.
   Google Scholar