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Articles

Non-convex ℓp regularization for sparse reconstruction of electrical impedance tomography

Pages 1032-1053 | Received 29 Mar 2019, Accepted 27 Aug 2020, Published online: 15 Sep 2020

References

  • Vauhkonen M, Vadsz D, Karjalainen PA, et al. Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans Med Imaging. 1998;17(2):285–293.
  • Borsic A, Graham BM, Adler A, et al. Total variation regularization in electrical impedance tomography. Inv Probl. 2007;99:A12.
  • Hinze M, Kaltenbacher B, Quyen TNT. Identifying conductivity in electrical impedance tomography with total variation regularization. Numerische Mathematik. 2018;138(3):723–765.
  • 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.
  • Wang J, Ma J, Han B, et al. Split Bregman iterative algorithm for sparse reconstruction of electrical impedance tomography. Signal Process. 2012;92(12):2952–2961.
  • Gehre M, Kluth T, Sebu C, et al. Sparse 3D reconstructions in electrical impedance tomography using real data. Inv Prob Sci Eng. 2014;22(1):31–44.
  • Pham Muoi Q. Reconstructing conductivity coefficients based on sparsity regularization and measured data in electrical impedance tomography. Inv Prob Sci Eng. 2015;23(8):1366–1387.
  • Garde H, Knudsen K. Sparsity prior for electrical impedance tomography with partial data. Inv Prob Sci Eng. 2016;24(3):524–541.
  • 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.
  • Liu J, Ling L, Li G. A novel combined regularization algorithm of total variation and Tikhonov regularization for open electrical impedance tomography. Phys Meas. 2013;34(7):823.
  • Wang J, Han B, Wang W. Elastic-net regularization for nonlinear electrical impedance tomography with a splitting approach. Appl Anal. 2019;98(12):2201–2217.
  • Chartrand R. Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Process Lett. 2007;14(10):707–710.
  • Nikolova M, Ng M, Zhang S, et al. Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization. SIAM J Imaging Sci. 2008;1(1):2–25.
  • Xu ZB, Zhang H, Wang Y, et al. L1/2 regularization. Sci China Series F (Inf Sci),. 2010;53(6):1159–1169.
  • Chen X, Xu F, Ye Y. Lower bound theory of nonzero entries in solutions of l2−lp minimization. SIAM J Sci Comput. 2010;32(5):2832–2852.
  • Lai MJ, Wang J. An unconstrained lq minimization with 0<q≤1 for sparse solution of underdetermined linear systems. SIAM J Optim. 2011;21(1):82–101.
  • Ge D, Jiang X, Ye Y. A note on the complexity of ℓp minimization. Math Program. 2011;129(2):285–299.
  • Chen X, Zhou W. Convergence of the reweighted ℓ1 minimization algorithm for ℓ2−ℓp minimization. Comput Optim Appl. 2014;59(1–2):47–61.
  • Lu Z. Iterative reweighted minimization methods for lp regularized unconstrained nonlinear programming. Math Program. 2014;147(1–2):277–307.
  • Chen X, Zhou W. Smoothing nonlinear conjugate gradient method for image restoration using nonsmooth nonconvex minimization. SIAM J Imaging Sci. 2010;3(4):765–790.
  • Chen X. Smoothing methods for nonsmooth. nonconvex minimization. Math Program. 2012;134(1):71–99.
  • 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.
  • Woo EJ, Hua P, Webster JG, et al. Finite-element method in electrical impedance tomography. Med Biol Eng Comput. 1994;32(5):530–536.
  • Chen X, Ge D, Wang Z, et al. Complexity of unconstrained ℓ2- ℓp minimization. Math Program. 2014;143(1–2):371–383.
  • Huber PJ. Robust statistics. New York (NY): John Wiley and Sons; 1981.
  • Black MJ, Rangarajan A. On the unification of line processes, outlier rejection, and robust statistics with applications in early vision. Int J Comp Vis. 1996;19(1):57–91.
  • Lechleiter A, Rieder A. Newton regularizations for impedance tomography: convergence by local injectivity. Inv Prob. 2008;24(6):065009.
  • Jin B, Maass P. An analysis of electrical impedance tomography with, applications to Tikhonov regularization. ESAIM Control Optim Calcul Var. 2012;18(4):1027–1048.
  • He JH. Homotopy perturbation technique. Comp Methods Appl Mech Eng. 1999;178(3–4):257–262.
  • He JH. Homotopy perturbation method for bifurcation of nonlinear problems. Int J Nonlin Sci Numer Simul. 2005;6(2):207–208.
  • Jafari H, Momani S. Solving fractional diffusion and wave equations by modified homotopy perturbation method. Phys Lett A. 2007;370(5–6):388–396.
  • Cao L, Han B, Wang W. Homotopy perturbation method for nonlinear ill-posed operator equations. Int J Nonlin Sci Numer Simul. 2009;10(10):1319–1322.
  • Wang J, Wang W, Han B. An iteration regularization method with general convex penalty for nonlinear inverse problems in Banach spaces. J Comput Appl Math. 2019;361:472–486.
  • Long H, Han B, Tong S. A new Kaczmarz type method and its acceleration for nonlinear ill-posed problems. Inv Probl. 2019;35:055004.
  • Jin Q, Wang W. Landweber iteration of Kaczmarz type with general non-smooth convex penalty functionals. Inv Probl. 2013;29(8):085011.
  • Vauhkonen M, Lionheart WRB, Heikkinen LM, et al. A matlab package for the EIDORS project to reconstruct two-dimensional EIT images. Physiol Meas. 2001;22(1):107–111.

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