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Erschienen in: Medical & Biological Engineering & Computing 8/2016

01.08.2016 | Original Article

A fast time-difference inverse solver for 3D EIT with application to lung imaging

verfasst von: Ashkan Javaherian, Manuchehr Soleimani, Knut Moeller

Erschienen in: Medical & Biological Engineering & Computing | Ausgabe 8/2016

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Abstract

A class of sparse optimization techniques that require solely matrix–vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.

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Literatur
1.
Zurück zum Zitat Adler A, Guardo R (1996) Electrical impedance tomography: regularized imaging and contrast detection. IEEE Trans Biomed Eng 15:170–179 Adler A, Guardo R (1996) Electrical impedance tomography: regularized imaging and contrast detection. IEEE Trans Biomed Eng 15:170–179
2.
Zurück zum Zitat Adler A, Arnold JH, Bayford R, Borsic A, Brown B, Dixon P, Faes TJC, Frerichs I, Gagnon H, Gärber Y, Grychtol B, Hahn G, Lionheart WRB, Malik A, Patterson RP, Stocks J, Tizzard A, Weiler N, Wolf GK (2009) GREIT: a unified approach to 2D linear EIT reconstruction of lung images. Physiol Meas 30(6):35–55CrossRef Adler A, Arnold JH, Bayford R, Borsic A, Brown B, Dixon P, Faes TJC, Frerichs I, Gagnon H, Gärber Y, Grychtol B, Hahn G, Lionheart WRB, Malik A, Patterson RP, Stocks J, Tizzard A, Weiler N, Wolf GK (2009) GREIT: a unified approach to 2D linear EIT reconstruction of lung images. Physiol Meas 30(6):35–55CrossRef
3.
Zurück zum Zitat Adler A, Amato MB, Arnold JH, Bayford R, Bodenstein M, Böhm SH, Brown BH, Frerichs I, Stenqvist O, Weiler N, Wolf GK (2012) Whither Lung EIT: where are we, where do we want to go and what do we need to get there? Physiol Meas 33(5):679–694CrossRefPubMed Adler A, Amato MB, Arnold JH, Bayford R, Bodenstein M, Böhm SH, Brown BH, Frerichs I, Stenqvist O, Weiler N, Wolf GK (2012) Whither Lung EIT: where are we, where do we want to go and what do we need to get there? Physiol Meas 33(5):679–694CrossRefPubMed
4.
Zurück zum Zitat Bagshaw AP, Liston AD, Bayford RH, Tizzard A, Gibson AP, Tidswell T, Sparkes MK, Dehghani H, Binnie CD, Holder DS (2003) Electrical impedance tomography of human brain function using reconstruction algorithms based on the finite element method. Neuro Image 20:752–764PubMed Bagshaw AP, Liston AD, Bayford RH, Tizzard A, Gibson AP, Tidswell T, Sparkes MK, Dehghani H, Binnie CD, Holder DS (2003) Electrical impedance tomography of human brain function using reconstruction algorithms based on the finite element method. Neuro Image 20:752–764PubMed
5.
Zurück zum Zitat Barber DC, Brown BH (1988) Errors in reconstruction of resistivity images using a linear reconstruction technique. Clin Phys Physiol Meas 9:101–104CrossRefPubMed Barber DC, Brown BH (1988) Errors in reconstruction of resistivity images using a linear reconstruction technique. Clin Phys Physiol Meas 9:101–104CrossRefPubMed
6.
Zurück zum Zitat Barzilai J, Borwein J (1988) Two point step size gradient methods. IMA J Numer Anal 8:141–148CrossRef Barzilai J, Borwein J (1988) Two point step size gradient methods. IMA J Numer Anal 8:141–148CrossRef
7.
Zurück zum Zitat Bertsekas DP (1999) Nonlinear programming, 2nd edn. Athena, Boston Bertsekas DP (1999) Nonlinear programming, 2nd edn. Athena, Boston
8.
Zurück zum Zitat Bioucas-Dias J, Figueiredo M (2007) A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Trans Image Process 16(12):2992–3004CrossRefPubMed Bioucas-Dias J, Figueiredo M (2007) A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Trans Image Process 16(12):2992–3004CrossRefPubMed
9.
Zurück zum Zitat Blue RS, Isaacson D, Newell JC (2000) Real-time three-dimensional electrical impedance imaging. Physiol Meas 21:1–12CrossRef Blue RS, Isaacson D, Newell JC (2000) Real-time three-dimensional electrical impedance imaging. Physiol Meas 21:1–12CrossRef
10.
Zurück zum Zitat Borsic A, Lionheart WRB, McLeod CN (2002) Generation of anisotropic-smoothness regularization filters for EIT. IEEE Trans Med Imag 21(6):579–587CrossRef Borsic A, Lionheart WRB, McLeod CN (2002) Generation of anisotropic-smoothness regularization filters for EIT. IEEE Trans Med Imag 21(6):579–587CrossRef
11.
Zurück zum Zitat Borsic A, Graham BM, Adler A, Lionheart WRB (2010) In vivo impedance imaging with total variation regularization. IEEE Trans Med Imag 29(1):44–54CrossRef Borsic A, Graham BM, Adler A, Lionheart WRB (2010) In vivo impedance imaging with total variation regularization. IEEE Trans Med Imag 29(1):44–54CrossRef
12.
13.
Zurück zum Zitat Chen S, Donoho D, Saunders M (1998) Atomic decomposition by basis pursuit. SIAM J Sci Comput 20:33–61CrossRef Chen S, Donoho D, Saunders M (1998) Atomic decomposition by basis pursuit. SIAM J Sci Comput 20:33–61CrossRef
14.
Zurück zum Zitat Cheney M, Isaacson D, Newell JC, Simske S, Goble J (1990) NOSER: an algorithm for solving the inverse conductivity problem. Int J Imaging Syst Technol 2:66–75CrossRef Cheney M, Isaacson D, Newell JC, Simske S, Goble J (1990) NOSER: an algorithm for solving the inverse conductivity problem. Int J Imaging Syst Technol 2:66–75CrossRef
15.
Zurück zum Zitat Cheney M, Isaacson D, Newell JC (1999) Electrical impedance tomography. SIAM Rev 41:85–101CrossRef Cheney M, Isaacson D, Newell JC (1999) Electrical impedance tomography. SIAM Rev 41:85–101CrossRef
16.
Zurück zum Zitat Cuadros AP, Arce GR, Arguello H (2014) Coded aperture design in compressive X-ray tomography. In: IEEE global conference on signal and information processing, 3–5 Dec 2014 Cuadros AP, Arce GR, Arguello H (2014) Coded aperture design in compressive X-ray tomography. In: IEEE global conference on signal and information processing, 3–5 Dec 2014
17.
Zurück zum Zitat Dobson DC, Santosa F (1994) An image enhancement technique for electrical impedance tomography. Inverse Probl 10:317–334CrossRef Dobson DC, Santosa F (1994) An image enhancement technique for electrical impedance tomography. Inverse Probl 10:317–334CrossRef
20.
Zurück zum Zitat Fan WR, Wang HX (2010) 3D modeling of the human thorax for ventilation distribution measured through electrical impedance tomography. Meas Sci Technol 21:115801CrossRef Fan WR, Wang HX (2010) 3D modeling of the human thorax for ventilation distribution measured through electrical impedance tomography. Meas Sci Technol 21:115801CrossRef
21.
Zurück zum Zitat Figueiredo M, Nowak R, Wright S (2007) Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J Sel Top Signal Process 1:586–598CrossRef Figueiredo M, Nowak R, Wright S (2007) Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J Sel Top Signal Process 1:586–598CrossRef
22.
Zurück zum Zitat Gehre M, Kluth T, Lipponen A, Jin B, Seppänen A, Kaipio JP, Maass P (2012) Sparsity reconstruction in electrical impedance tomography: an experimental evaluation. J Comput Appl Math 236:2126–2136CrossRef Gehre M, Kluth T, Lipponen A, Jin B, Seppänen A, Kaipio JP, Maass P (2012) Sparsity reconstruction in electrical impedance tomography: an experimental evaluation. J Comput Appl Math 236:2126–2136CrossRef
23.
Zurück zum Zitat Gehre M, Kluth T, Sebu C, Maass P (2014) Sparse 3D reconstructions in electrical impedance tomography using real data. Inverse Probl Sci Eng 22(1):31–44CrossRef Gehre M, Kluth T, Sebu C, Maass P (2014) Sparse 3D reconstructions in electrical impedance tomography using real data. Inverse Probl Sci Eng 22(1):31–44CrossRef
24.
Zurück zum Zitat Gobel JC, Cheney M, Isaacson D (1992) Electrical impedance tomography in three dimensions. Appl Comput Electromagn Soc J 7:128–147 Gobel JC, Cheney M, Isaacson D (1992) Electrical impedance tomography in three dimensions. Appl Comput Electromagn Soc J 7:128–147
25.
Zurück zum Zitat Goharian M, Soleimani M, Moran G (2009) A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data. Prog Electromagn Res 94:19–32CrossRef Goharian M, Soleimani M, Moran G (2009) A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data. Prog Electromagn Res 94:19–32CrossRef
27.
Zurück zum Zitat Graham BM, Adler A (2007) Electrode placement configurations for 3D EIT. Physiol Meas 28:29–44CrossRef Graham BM, Adler A (2007) Electrode placement configurations for 3D EIT. Physiol Meas 28:29–44CrossRef
28.
Zurück zum Zitat Hale T, Yin W, Zhang Y (2007) A fixed-point continuation method for l 1-regularized minimization with applications to compressed sensing. Department of Computational and Applied Mathematics, Rice University, Houston, TX, Technical Report TR07-07 Hale T, Yin W, Zhang Y (2007) A fixed-point continuation method for l 1-regularized minimization with applications to compressed sensing. Department of Computational and Applied Mathematics, Rice University, Houston, TX, Technical Report TR07-07
29.
Zurück zum Zitat Halter RJ, Hartov A, Paulsen KD (2007) Experimental justification for using 3D conductivity reconstructions in electrical impedance tomography. Physiol Meas 28:115–127CrossRef Halter RJ, Hartov A, Paulsen KD (2007) Experimental justification for using 3D conductivity reconstructions in electrical impedance tomography. Physiol Meas 28:115–127CrossRef
30.
Zurück zum Zitat Halter RJ, Hartov A, Paulsen KD (2008) A broadband high-frequency electrical impedance tomography system for breast imaging. IEEE Trans Biomed Eng 55(2):650–659CrossRefPubMed Halter RJ, Hartov A, Paulsen KD (2008) A broadband high-frequency electrical impedance tomography system for breast imaging. IEEE Trans Biomed Eng 55(2):650–659CrossRefPubMed
31.
Zurück zum Zitat He X, Liang J, Wang X, Yu J, Qu X, Wang X, Hou Y, Chen D, Liu F, Tian J (2010) Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method. Opt Express 18(24):24825–24841CrossRefPubMed He X, Liang J, Wang X, Yu J, Qu X, Wang X, Hou Y, Chen D, Liu F, Tian J (2010) Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method. Opt Express 18(24):24825–24841CrossRefPubMed
32.
Zurück zum Zitat Holder DS (2004) Electrical impedance tomography: methods, history and applications. Institute of Physics Publishing, pp 3–64 Holder DS (2004) Electrical impedance tomography: methods, history and applications. Institute of Physics Publishing, pp 3–64
33.
Zurück zum Zitat Horesh L, Bolhofer M, Schweiger M, Arridge SR, Holder DS (2007) Novel large-scale 3D electrical impedance tomography modeling of the human head. IFMBE Proc 14:3858–3861CrossRef Horesh L, Bolhofer M, Schweiger M, Arridge SR, Holder DS (2007) Novel large-scale 3D electrical impedance tomography modeling of the human head. IFMBE Proc 14:3858–3861CrossRef
34.
Zurück zum Zitat Howland GA, Lum DJ, Howell JC (2014) Compressive wavefront sensing with weak values. Opt Express 22(16):18870–18880CrossRefPubMed Howland GA, Lum DJ, Howell JC (2014) Compressive wavefront sensing with weak values. Opt Express 22(16):18870–18880CrossRefPubMed
35.
Zurück zum Zitat Javaherian A, Soleimani M (2013) Compressed sampling for boundary measurements in three-dimensional electrical impedance tomography. Physiol Meas 34:1133–1150CrossRefPubMed Javaherian A, Soleimani M (2013) Compressed sampling for boundary measurements in three-dimensional electrical impedance tomography. Physiol Meas 34:1133–1150CrossRefPubMed
36.
Zurück zum Zitat Javaherian A, Movafeghi A, Faghihi R (2013) Reducing negative effects of quadratic norm regularization on image reconstruction in electrical impedance tomography. Appl Math Model 37(8):5637–5652CrossRef Javaherian A, Movafeghi A, Faghihi R (2013) Reducing negative effects of quadratic norm regularization on image reconstruction in electrical impedance tomography. Appl Math Model 37(8):5637–5652CrossRef
37.
Zurück zum Zitat Javaherian A, Soleimani M, Moeller K (2015) Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography. Physiol Meas 36(1):43–66CrossRefPubMed Javaherian A, Soleimani M, Moeller K (2015) Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography. Physiol Meas 36(1):43–66CrossRefPubMed
38.
Zurück zum Zitat Jin B, Khan T, Maass P (2012) A reconstruction algorithm for electrical impedance tomography based on sparsity regularization. Int J Numer Methods Eng 89:337–353CrossRef Jin B, Khan T, Maass P (2012) A reconstruction algorithm for electrical impedance tomography based on sparsity regularization. Int J Numer Methods Eng 89:337–353CrossRef
39.
Zurück zum Zitat Kim SJ, Koh K, Lustig M, Boyd S, Gorinevsky D (2007) An interior-point method for large-scale l 1-regularized least squares. IEEE J Sel Top Signal Process 1(4):606–617CrossRef Kim SJ, Koh K, Lustig M, Boyd S, Gorinevsky D (2007) An interior-point method for large-scale l 1-regularized least squares. IEEE J Sel Top Signal Process 1(4):606–617CrossRef
40.
Zurück zum Zitat Lionheart WRB (2004) EIT reconstruction algorithms: pitfalls, challenges and recent developments. Physiol Meas 25:125–142CrossRefPubMed Lionheart WRB (2004) EIT reconstruction algorithms: pitfalls, challenges and recent developments. Physiol Meas 25:125–142CrossRefPubMed
41.
Zurück zum Zitat Mamatjan Y, Borsic A, Gursoy D, Adler Andy (2013) An experimental clinical evaluation of EIT imaging with l 1 data and image norms. Physiol Meas 34:1027–1039CrossRefPubMed Mamatjan Y, Borsic A, Gursoy D, Adler Andy (2013) An experimental clinical evaluation of EIT imaging with l 1 data and image norms. Physiol Meas 34:1027–1039CrossRefPubMed
42.
Zurück zum Zitat Metherall P, Barber DC, Smallwood RH, Brown BH (1996) Three dimensional electrical impedance tomography. Nature 380:509–512CrossRefPubMed Metherall P, Barber DC, Smallwood RH, Brown BH (1996) Three dimensional electrical impedance tomography. Nature 380:509–512CrossRefPubMed
44.
Zurück zum Zitat Park JC, Song B, Kim JS, Park SH, Kim HK, Liu Z, Suh TS, Song WY (2012) Fast compressed sensing-based CBCT reconstruction using Barzilai–Borwein formulation for application to on-line IGRT. Med Phys 39(3):1207–1217CrossRefPubMed Park JC, Song B, Kim JS, Park SH, Kim HK, Liu Z, Suh TS, Song WY (2012) Fast compressed sensing-based CBCT reconstruction using Barzilai–Borwein formulation for application to on-line IGRT. Med Phys 39(3):1207–1217CrossRefPubMed
45.
Zurück zum Zitat Rezajoo S, Hossein-Zadeh G (2010) Reconstruction convergence and speed enhancement in electrical impedance tomography for domains with known internal boundaries. Physiol Meas 31:1499–1516CrossRefPubMed Rezajoo S, Hossein-Zadeh G (2010) Reconstruction convergence and speed enhancement in electrical impedance tomography for domains with known internal boundaries. Physiol Meas 31:1499–1516CrossRefPubMed
46.
Zurück zum Zitat Shewchuk JR (1994) An introduction to the conjugate gradient method without the agonizing pain. Carnegie Mellon University, Pittsburgh Shewchuk JR (1994) An introduction to the conjugate gradient method without the agonizing pain. Carnegie Mellon University, Pittsburgh
47.
Zurück zum Zitat Soleimani M, Gomez-Laberge C, Adler A (2006) Imaging of conductivity changes and electrode movement in EIT. Physiol Meas 27:103–113CrossRef Soleimani M, Gomez-Laberge C, Adler A (2006) Imaging of conductivity changes and electrode movement in EIT. Physiol Meas 27:103–113CrossRef
48.
Zurück zum Zitat Thompson D, Harmany Z, Marciat R (2011) Sparse video recovery using linearly constrained gradient projection. In: IEEE international conference on acoustic, speech and signal processing (ICASSP), Prague, Czech, 22–27 May 2011 Thompson D, Harmany Z, Marciat R (2011) Sparse video recovery using linearly constrained gradient projection. In: IEEE international conference on acoustic, speech and signal processing (ICASSP), Prague, Czech, 22–27 May 2011
49.
Zurück zum Zitat Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc B 58:267–288 Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc B 58:267–288
50.
Zurück zum Zitat Vauhkonen M, Vadasz D, Karjalainen PA, Somersalo E, Kaipio JP (1998) Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans Med Imag 17(2):285–293CrossRef Vauhkonen M, Vadasz D, Karjalainen PA, Somersalo E, Kaipio JP (1998) Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans Med Imag 17(2):285–293CrossRef
51.
Zurück zum Zitat Vauhkonen PJ, Vauhkonen M, Savolainen T, Kaipio JP (1999) Three dimensional electrical impedance tomography based on the complete electrode model. IEEE Trans Biomed Eng 46:1150–1160CrossRefPubMed Vauhkonen PJ, Vauhkonen M, Savolainen T, Kaipio JP (1999) Three dimensional electrical impedance tomography based on the complete electrode model. IEEE Trans Biomed Eng 46:1150–1160CrossRefPubMed
52.
Zurück zum Zitat Wright SJ, Nowak RD, Figueiredo MAT (2009) Sparse reconstruction by separable approximation. IEEE Trans Signal Process 57:2479–2493CrossRef Wright SJ, Nowak RD, Figueiredo MAT (2009) Sparse reconstruction by separable approximation. IEEE Trans Signal Process 57:2479–2493CrossRef
53.
Zurück zum Zitat Xiao B, Harker PT (1989) Perturbation results for the linear complementarity problem. Appl Math Lett 2(4):401–405CrossRef Xiao B, Harker PT (1989) Perturbation results for the linear complementarity problem. Appl Math Lett 2(4):401–405CrossRef
54.
Zurück zum Zitat Xu X, Li E, Yu H, Gong W, Han S (2014) Morphology separation in ghost imaging via sparsity constraint. Opt Express 22(12):14375–14381CrossRefPubMed Xu X, Li E, Yu H, Gong W, Han S (2014) Morphology separation in ghost imaging via sparsity constraint. Opt Express 22(12):14375–14381CrossRefPubMed
55.
Zurück zum Zitat Yang CL, Wei HY, Adler A, Soleimani M (2013) Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction. Physiol Meas 34:645–658CrossRefPubMed Yang CL, Wei HY, Adler A, Soleimani M (2013) Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction. Physiol Meas 34:645–658CrossRefPubMed
56.
Zurück zum Zitat Yorkey TJ, Webster JG, Tompkins WJ (1987) Comparing reconstruction algorithms for electrical impedance tomography. IEEE Trans Biomed Eng 34:843–852CrossRefPubMed Yorkey TJ, Webster JG, Tompkins WJ (1987) Comparing reconstruction algorithms for electrical impedance tomography. IEEE Trans Biomed Eng 34:843–852CrossRefPubMed
57.
Zurück zum Zitat Yu Y, Hong M, Liu F, Wang H, Crozier S (2010) Comparison and analysis of nonlinear algorithms for compressed sensing in MRI. In: 32nd annual international conference of the IEEE EMBS, Buenos Aires, Argentina, September 2010 Yu Y, Hong M, Liu F, Wang H, Crozier S (2010) Comparison and analysis of nonlinear algorithms for compressed sensing in MRI. In: 32nd annual international conference of the IEEE EMBS, Buenos Aires, Argentina, September 2010
Metadaten
Titel
A fast time-difference inverse solver for 3D EIT with application to lung imaging
verfasst von
Ashkan Javaherian
Manuchehr Soleimani
Knut Moeller
Publikationsdatum
01.08.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Medical & Biological Engineering & Computing / Ausgabe 8/2016
Print ISSN: 0140-0118
Elektronische ISSN: 1741-0444
DOI
https://doi.org/10.1007/s11517-015-1441-1

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