American Institute of Mathematical Sciences

Advanced
June  2022, 16(3): 647-671. doi: 10.3934/ipi.2021066

Automated filtering in the nonlinear Fourier domain of systematic artifacts in 2D electrical impedance tomography

Melody Alsaker 1,, , Benjamin Bladow 2, , Scott E. Campbell 3, and  Emma M. Kar 4,

1. 

Department of Mathematics, Gonzaga University, Spokane, WA 99258, USA
2. 

Boeing Co., 6001 S Air Depot Blvd, Oklahoma City, OK 73135, USA
3. 

Department of Physics & Astronomy, Michigan State University, East Lansing, MI 48824, USA
4. 

College of Medicine, University of Arizona, Phoenix, AZ 85004, USA

*Corresponding author: Melody Alsaker

Received  July 2021 Revised  August 2021 Published  June 2022 Early access  October 2021

For patients undergoing mechanical ventilation due to respiratory failure, 2D electrical impedance tomography (EIT) is emerging as a means to provide functional monitoring of pulmonary processes. In EIT, electrical current is applied to the body, and the internal conductivity distribution is reconstructed based on subsequent voltage measurements. However, EIT images are known to often suffer from large systematic artifacts arising from various limitations and exacerbated by the ill-posedness of the inverse problem. The direct D-bar reconstruction method admits a nonlinear Fourier analysis of the EIT problem, providing the ability to process and filter reconstructions in the nonphysical frequency regime. In this work, a technique is introduced for automated Fourier-domain filtering of known systematic artifacts in 2D D-bar reconstructions. The new method is validated using three numerically simulated static thoracic datasets with induced artifacts, plus two experimental dynamic human ventilation datasets containing systematic artifacts. Application of the method is shown to significantly reduce the appearance of artifacts and improve the shape of the lung regions in all datasets.

Keywords: Electrical impedance tomography, image reconstruction, Fourier domain filtering, D-bar methods, artifact removal.
Mathematics Subject Classification: Primary: 92C55; Secondary: 65N21.
Citation: Melody Alsaker, Benjamin Bladow, Scott E. Campbell, Emma M. Kar. Automated filtering in the nonlinear Fourier domain of systematic artifacts in 2D electrical impedance tomography. Inverse Problems and Imaging, 2022, 16 (3) : 647-671. doi: 10.3934/ipi.2021066
References:
[1]

A. Adler, R. Guardo and Y. Berthiaume, Impedance imaging of lung ventilation: Do we need to account for chest expansion?, IEEE Tran. Biomedical Engineering, 43 (1994), 414-420.  doi: 10.1109/IEMBS.1994.411917.

[2]

A. Adler et al., GREIT: A unified approach to 2D linear EIT reconstruction of lung images, Physiological Measurement, 30 (2009), 35pp.

[3]

G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal., 27 (1988), 153-172.  doi: 10.1080/00036818808839730.

[4]

M. Alsaker and J. Mueller, A D-bar algorithm with a priori information for 2-dimensional electrical impedance tomography, SIAM J. Imaging Sci, 9 (2016), 1619-1654.  doi: 10.1137/15M1020137.

[5]

M. Alsaker, D. A. C. Cárdenas, S. S. Furuie and J. L. Mueller, Complementary use of priors for pulmonary imaging with electrical impedance and ultrasound computed tomography, J. Compu. Appl. Math., 395 (2021), 15pp. doi: 10.1016/j.cam.2021.113591.

[6]

M. Alsaker and J. L. Mueller, Use of an optimized spatial prior in D-bar reconstructions of EIT tank data, Inverse Probl. Imaging, 12 (2018), 883-901.  doi: 10.3934/ipi.2018037.

[7]

M. Alsaker, J. L. Mueller and R. Murthy, Dynamic optimized priors for D-bar reconstructions of human ventilation using electrical impedance tomography, J. Comput. Appl. Math., 362 (2019), 276-294.  doi: 10.1016/j.cam.2018.07.039.

[8]

N. Avis and D. Barber, Incorporating a priori information into the Sheffield filtered backprojection algorithm, Physiological Measurement, 16 (1995). doi: 10.1088/0967-3334/16/3A/011.

[9]

R. H. Bayford, Bioimpedance tomography (electrical impedance tomography), Annu. Rev. Biomed. Eng., 8 (2006), 63-91.  doi: 10.1146/annurev.bioeng.8.061505.095716.

[10]

R. Blue, D. Isaacson and J. C. Newell, Real-time three-dimensional electrical impedance imaging, Physiological Measurement, 21 (2000), 15pp. doi: 10.1088/0967-3334/21/1/303.

[11]

K. Boone and D. Holder, Effect of skin impedance on image quality and variability in electrical impedance tomography: A model study, Medical and Biological Engineering and Computing, 34 (1996), 351-354.  doi: 10.1007/BF02520003.

[12]

A. Boyle and A. Adler, Electrode models under shape deformation in electrical impedance tomography, J. Phys.: Conf. Ser., 224 (2010). doi: 10.1088/1742-6596/224/1/012051.

[13]

A. Boyle, A. Adler and W. R. Lionheart, Shape deformation in two-dimensional electrical impedance tomography, IEEE Tran. Med. Imaging, 31 (2012), 2185-2193.  doi: 10.1109/TMI.2012.2204438.

[14]

C. Bozsak and E. Techner, Mini-Manual Electrical Impedance Tomography (EIT): Device Handling, Application Tips, and Examples, 2018. https://www.draeger.com/Library/Content/EIT-Mini-Manual.pdf

[15]

M. Cheney, D. Isaacson, J. C. Newell, S. Simske and J. Goble, NOSER: An algorithm for solving the inverse conductivity problem, Inter. J. Imaging Systems and Technology, 2 (1990), 66-75. 

[16]

T. de Castro Martins, et al., A review of electrical impedance tomography in lung applications: Theory and algorithms for absolute images, Annual Reviews in Control.

[17]

H. Dehghani, D. Barber and I. Basarab-Horwath, Incorporating a priori anatomical information into image reconstruction in electrical impedance tomography, Physiological Measurement, 20 (1999), 87pp.

[18]

M. Dodd and J. Mueller, A real-time D-bar algorithm for 2-D electrical impedance tomography data, Inverse Probl. Imaging, 8 (2014), 1013-1031.  doi: 10.3934/ipi.2014.8.1013.

[19]

S. Guan, A. A. Khan, S. Sikdar and P. V. Chitnis, Fully dense UNet for 2-D sparse photoacoustic tomography artifact removal, IEEE J. Biomedical and Health Informatics, 24 (2019), 568-576.  doi: 10.1109/JBHI.2019.2912935.

[20]

R. Guardo, C. Boulay, B. Murray and M. Bertrand, An experimental study in electrical impedance tomography using backprojection reconstruction, IEEE Tran., 38 (1991), 617-627.  doi: 10.1109/10.83560.

[21]

S. Hamilton and A. Hauptmann, Deep d-bar: Real-time electrical impedance tomography imaging with deep neural networks, IEEE Trans. Med. Imaging., 37 (2018), 2367-2377.  doi: 10.1109/TMI.2018.2828303.

[22]

Y. Hayashi et al., Toward improved surveillance: The impact of ventilator-associated complications on length of stay and antibiotic use in patients in intensive care units, Clinical Infectious Diseases, 56 (2013), 471-477. 

[23]

P. Hua, E. J. Woo, J. G. Webster and W. J. Tompkins, Iterative reconstruction methods using regularization and optimal current patterns in electrical impedance tomography, IEEE Trans. Med. Imaging, 10 (1991), 621-628.  doi: 10.1109/42.108598.

[24]

J. P. Kaipio, V. Kolehmainen, M. Vauhkonen and E. Somersalo, Inverse problems with structural prior information, Inverse Problems, 15 (1999), 713-729.  doi: 10.1088/0266-5611/15/3/306.

[25]

K. Knudsen, M. Lassas, J. L. Mueller and S. Siltanen, Regularized D-bar method for the inverse conductivity problem, Inverse Probl. Imaging., 3 (2009), 599-624.  doi: 10.3934/ipi.2009.3.599.

[26]

J. Kobylianskii, A. Murray, D. Brace, E. Goligher and E. Fan, Electrical impedance tomography in adult patients undergoing mechanical ventilation: A systematic review, J. Critical Care, 35 (2016), 33-50.  doi: 10.1016/j.jcrc.2016.04.028.

[27]

V. Kolehmainen, M. Vauhkonen, P. Karjalainen and J. Kaipio, Assessment of errors in static electrical impedance tomography with adjacent and trigonometric current patterns, Physiological Measurement, 18 (1997). doi: 10.1088/0967-3334/18/4/003.

[28]

V. Kolehmainen, M. Lassas and P. Ola, Electrical impedance tomography problem with inaccurately known boundary and contact impedances, IEEE Trans. Med. Imaging, 27 (2006), 1404-1414.  doi: 10.1109/ISBI.2006.1625120.

[29]

K. Lee, E. J. Woo and J. K. Seo, A fidelity-embedded regularization method for robust electrical impedance tomography, IEEE Trans. Med. Imaging, 37 (2018), 1970-1977.  doi: 10.1109/TMI.2017.2762741.

[30]

S. Leonhardt and B. Lachmann, Electrical impedance tomography: The holy grail of ventilation and perfusion monitoring?, Intensive Care Medicine, 38 (2012), 1917-1929.  doi: 10.1007/s00134-012-2684-z.

[31]

D. Liu and J. Du, A moving morphable components based shape reconstruction framework for electrical impedance tomography, IEEE Trans. Med. Imaging, 38 (2019), 2937-2948.  doi: 10.1109/TMI.2019.2918566.

[32]

D. Liu, V. Kolehmainen, S. Siltanen, A.-M. Laukkanen and A. Seppänen, Nonlinear difference imaging approach to three-dimensional electrical impedance tomography in the presence of geometric modeling errors, IEEE Trans. Biomedical Engineering, 63 (2016), 1956-1965.  doi: 10.1109/TBME.2015.2509508.

[33]

D. Liu, D. Smyl, D. Gu and J. Du, Shape-driven difference electrical impedance tomography, IEEE Trans. Med. Imaging, 39 (2020), 3801-3812.  doi: 10.1109/TMI.2020.3004806.

[34]

S. Liu, R. Cao, Y. Huang, T. Ouypornkochagorn and J. Jia, Time sequence learning for electrical impedance tomography using bayesian spatiotemporal priors, IEEE Trans. Instrumentation and Measurement, 69 (2020), 6045-6057.  doi: 10.1109/TIM.2020.2972172.

[35]

S. Liu, J. Jia, Y. D. Zhang and Y. Yang, Image reconstruction in electrical impedance tomography based on structure-aware sparse bayesian learning, IEEE Trans. Med. Imaging, 37 (2018), 2090-2102.  doi: 10.1109/TMI.2018.2816739.

[36]

S. Liu, J. Jia, Y. D. Zhang and Y. Yang, Image reconstruction in electrical impedance tomography based on structure-aware sparse bayesian learning, IEEE Trans. Med. Imaging, 37 (2018), 2090-2102.  doi: 10.1109/TMI.2018.2816739.

[37]

A. Lyckegaard, G. Johnson and P. Tafforeau, Correction of ring artifacts in X-ray tomographic images, Int. J. Tomo. Stat, 18 (2011), 1-9. 

[38]

S. Martin and C. T. M. Choi, A post-processing method for three-dimensional electrical impedance tomography, Scientific Reports, 7 (2017). doi: 10.1038/s41598-017-07727-2.

[39]

T. Mauri, A. Mercat and G. Grasselli, What's new in electrical impedance tomography, Intensive Care Medicine, 45 (2019), 674-677.  doi: 10.1007/s00134-018-5398-z.

[40]

M. M. Mellenthin et al., The ace1 electrical impedance tomography system for thoracic imaging, IEEE Tran. Instrumentation and Measurement, 68 (2019), 3137-3150. 

[41]

J. L. Mueller and S. Siltanen, Linear and Nonlinear Inverse Problems with Practical Applications, Computational Science & Engineering, 10. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2012. doi: 10.1137/1.9781611972344.

[42]

P. A. Muller, J. L. Mueller and M. M. Mellenthin, Real-time implementation of calderón's method on subject-specific domains, IEEE Tran. Medical Imaging, 36 (2017), 1868-1875. 

[43]

E. K. Murphy and J. L. Mueller, Effect of domain shape modeling and measurement errors on the 2-d d-bar method for eit, IEEE Tran. Med. Imaging, 28 (2009), 1576-1584.  doi: 10.1109/TMI.2009.2021611.

[44]

A. I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. Math., 143 (1996), 71-96.  doi: 10.2307/2118653.

[45]

S. Oh, T. Tang and R. Sadleir, Quantitative analysis of shape change in electrical impedance tomography (EIT), In 13th International Conference on Electrical Bioimpedance and the 8th Conference on Electrical Impedance Tomography, (2007), 424–427. doi: 10.1007/978-3-540-73841-1_110.

[46]

L. Pinhu, T. Whitehead, T. Evans and M. Griffiths, Ventilator-associated lung injury, The Lancet, 361 (2003), 332-340.  doi: 10.1016/S0140-6736(03)12329-X.

[47]

F. Sadi, S. Y. Lee and M. K. Hasan, Removal of ring artifacts in computed tomographic imaging using iterative center weighted median filter, Computers in Biology and Medicine, 40 (2010), 109-118.  doi: 10.1016/j.compbiomed.2009.11.007.

[48]

R. J. Sadleir and R. A. Fox, Detection and quantification of intraperitoneal fluid using electrical impedance tomography, IEEE Tran. Biomedical Engineering, 48 (2001), 484-491.  doi: 10.1109/10.915715.

[49]

S. Siltanen, J. Mueller and D. Isaacson, An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem, Inverse Probl., 16 (2000), 681-699.  doi: 10.1088/0266-5611/16/3/310.

[50]

N. K. Soni, H. Dehghani, A. Hartov and K. D. Paulsen, A novel data calibration scheme for electrical impedance tomography, Physiological Measurement, 24 (2003), 421-435.  doi: 10.1088/0967-3334/24/2/354.

[51]

N. K. Soni, A. Hartov, C. Kogel, S. P. Poplack and K. D. Paulsen, Multi-frequency electrical impedance tomography of the breast: New clinical results, Physiological Measurement, 25 (2004), 301-314.  doi: 10.1088/0967-3334/25/1/034.

[52]

E. Techner, M. Imhoff and S. Leonhardt, Electrical impedance tomography: Electrical impedance tomography: The realisation of regional ventilation monitoring, 2$^nd$ edition, 2015. https://www.draeger.com/Library/Content/EIT-Mini-Manual.pdf

[53]

V. Tomicic and R. Cornejo, Lung monitoring with electrical impedance tomography: Technical considerations and clinical applications, J. Thoracic Disease, 11 (2019), 3122-3155.  doi: 10.21037/jtd.2019.06.27.

[54]

S. Vergnole, G. Lamouche and M. L. Dufour, Artifact removal in fourier-domain optical coherence tomography with a piezoelectric fiber stretcher, Optics Letters, 33 (2008), 732-734.  doi: 10.1364/OL.33.000732.

[55]

T. Vu, M. Li, H. Humayun, Y. Zhou and J. Yao, A generative adversarial network for artifact removal in photoacoustic computed tomography with a linear-array transducer, Experimental Biology and Medicine, 245 (2020), 597-605.  doi: 10.1177/1535370220914285.

[56]

Z. Wang, A. Bovik, H. Sheikh and E. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Tran. Image Processing, 13 (2004), 600-612.  doi: 10.1109/TIP.2003.819861.

[57]

Y. Wu, B. Chen, K. Liu, C. Zhu, H. Pan, J. Jia, H. Wu and J. Yao, Shape reconstruction with multiphase conductivity for electrical impedance tomography using improved convolutional neural network method, IEEE Sensors Journal, 21 (2021), 9277-9287. 

[58]

G. Zhang et al., An on-line processing strategy for head movement interferences removal of dynamic brain electrical impedance tomography based on wavelet decomposition, Biomedical Engineering Online, 18 (2019).

[59]

Q. Zhang et al., Projection artifact removal improves visualization and quantitation of macular neovascularization imaged by optical coherence tomography angiography, Ophthalmology Retina, 1 (2017), 124-136. 

[60]

X. Zhang, J. Wang and L. Xing, Metal artifact reduction in x-ray computed tomography (CT) by constrained optimization, Medical Physics, 38 (2011), 701-711.  doi: 10.1118/1.3533711.

show all references

References:
[1]

A. Adler, R. Guardo and Y. Berthiaume, Impedance imaging of lung ventilation: Do we need to account for chest expansion?, IEEE Tran. Biomedical Engineering, 43 (1994), 414-420.  doi: 10.1109/IEMBS.1994.411917.

[2]

A. Adler et al., GREIT: A unified approach to 2D linear EIT reconstruction of lung images, Physiological Measurement, 30 (2009), 35pp.

[3]

G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal., 27 (1988), 153-172.  doi: 10.1080/00036818808839730.

[4]

M. Alsaker and J. Mueller, A D-bar algorithm with a priori information for 2-dimensional electrical impedance tomography, SIAM J. Imaging Sci, 9 (2016), 1619-1654.  doi: 10.1137/15M1020137.

[5]

M. Alsaker, D. A. C. Cárdenas, S. S. Furuie and J. L. Mueller, Complementary use of priors for pulmonary imaging with electrical impedance and ultrasound computed tomography, J. Compu. Appl. Math., 395 (2021), 15pp. doi: 10.1016/j.cam.2021.113591.

[6]

M. Alsaker and J. L. Mueller, Use of an optimized spatial prior in D-bar reconstructions of EIT tank data, Inverse Probl. Imaging, 12 (2018), 883-901.  doi: 10.3934/ipi.2018037.

[7]

M. Alsaker, J. L. Mueller and R. Murthy, Dynamic optimized priors for D-bar reconstructions of human ventilation using electrical impedance tomography, J. Comput. Appl. Math., 362 (2019), 276-294.  doi: 10.1016/j.cam.2018.07.039.

[8]

N. Avis and D. Barber, Incorporating a priori information into the Sheffield filtered backprojection algorithm, Physiological Measurement, 16 (1995). doi: 10.1088/0967-3334/16/3A/011.

[9]

R. H. Bayford, Bioimpedance tomography (electrical impedance tomography), Annu. Rev. Biomed. Eng., 8 (2006), 63-91.  doi: 10.1146/annurev.bioeng.8.061505.095716.

[10]

R. Blue, D. Isaacson and J. C. Newell, Real-time three-dimensional electrical impedance imaging, Physiological Measurement, 21 (2000), 15pp. doi: 10.1088/0967-3334/21/1/303.

[11]

K. Boone and D. Holder, Effect of skin impedance on image quality and variability in electrical impedance tomography: A model study, Medical and Biological Engineering and Computing, 34 (1996), 351-354.  doi: 10.1007/BF02520003.

[12]

A. Boyle and A. Adler, Electrode models under shape deformation in electrical impedance tomography, J. Phys.: Conf. Ser., 224 (2010). doi: 10.1088/1742-6596/224/1/012051.

[13]

A. Boyle, A. Adler and W. R. Lionheart, Shape deformation in two-dimensional electrical impedance tomography, IEEE Tran. Med. Imaging, 31 (2012), 2185-2193.  doi: 10.1109/TMI.2012.2204438.

[14]

C. Bozsak and E. Techner, Mini-Manual Electrical Impedance Tomography (EIT): Device Handling, Application Tips, and Examples, 2018. https://www.draeger.com/Library/Content/EIT-Mini-Manual.pdf

[15]

M. Cheney, D. Isaacson, J. C. Newell, S. Simske and J. Goble, NOSER: An algorithm for solving the inverse conductivity problem, Inter. J. Imaging Systems and Technology, 2 (1990), 66-75. 

[16]

T. de Castro Martins, et al., A review of electrical impedance tomography in lung applications: Theory and algorithms for absolute images, Annual Reviews in Control.

[17]

H. Dehghani, D. Barber and I. Basarab-Horwath, Incorporating a priori anatomical information into image reconstruction in electrical impedance tomography, Physiological Measurement, 20 (1999), 87pp.

[18]

M. Dodd and J. Mueller, A real-time D-bar algorithm for 2-D electrical impedance tomography data, Inverse Probl. Imaging, 8 (2014), 1013-1031.  doi: 10.3934/ipi.2014.8.1013.

[19]

S. Guan, A. A. Khan, S. Sikdar and P. V. Chitnis, Fully dense UNet for 2-D sparse photoacoustic tomography artifact removal, IEEE J. Biomedical and Health Informatics, 24 (2019), 568-576.  doi: 10.1109/JBHI.2019.2912935.

[20]

R. Guardo, C. Boulay, B. Murray and M. Bertrand, An experimental study in electrical impedance tomography using backprojection reconstruction, IEEE Tran., 38 (1991), 617-627.  doi: 10.1109/10.83560.

[21]

S. Hamilton and A. Hauptmann, Deep d-bar: Real-time electrical impedance tomography imaging with deep neural networks, IEEE Trans. Med. Imaging., 37 (2018), 2367-2377.  doi: 10.1109/TMI.2018.2828303.

[22]

Y. Hayashi et al., Toward improved surveillance: The impact of ventilator-associated complications on length of stay and antibiotic use in patients in intensive care units, Clinical Infectious Diseases, 56 (2013), 471-477. 

[23]

P. Hua, E. J. Woo, J. G. Webster and W. J. Tompkins, Iterative reconstruction methods using regularization and optimal current patterns in electrical impedance tomography, IEEE Trans. Med. Imaging, 10 (1991), 621-628.  doi: 10.1109/42.108598.

[24]

J. P. Kaipio, V. Kolehmainen, M. Vauhkonen and E. Somersalo, Inverse problems with structural prior information, Inverse Problems, 15 (1999), 713-729.  doi: 10.1088/0266-5611/15/3/306.

[25]

K. Knudsen, M. Lassas, J. L. Mueller and S. Siltanen, Regularized D-bar method for the inverse conductivity problem, Inverse Probl. Imaging., 3 (2009), 599-624.  doi: 10.3934/ipi.2009.3.599.

[26]

J. Kobylianskii, A. Murray, D. Brace, E. Goligher and E. Fan, Electrical impedance tomography in adult patients undergoing mechanical ventilation: A systematic review, J. Critical Care, 35 (2016), 33-50.  doi: 10.1016/j.jcrc.2016.04.028.

[27]

V. Kolehmainen, M. Vauhkonen, P. Karjalainen and J. Kaipio, Assessment of errors in static electrical impedance tomography with adjacent and trigonometric current patterns, Physiological Measurement, 18 (1997). doi: 10.1088/0967-3334/18/4/003.

[28]

V. Kolehmainen, M. Lassas and P. Ola, Electrical impedance tomography problem with inaccurately known boundary and contact impedances, IEEE Trans. Med. Imaging, 27 (2006), 1404-1414.  doi: 10.1109/ISBI.2006.1625120.

[29]

K. Lee, E. J. Woo and J. K. Seo, A fidelity-embedded regularization method for robust electrical impedance tomography, IEEE Trans. Med. Imaging, 37 (2018), 1970-1977.  doi: 10.1109/TMI.2017.2762741.

[30]

S. Leonhardt and B. Lachmann, Electrical impedance tomography: The holy grail of ventilation and perfusion monitoring?, Intensive Care Medicine, 38 (2012), 1917-1929.  doi: 10.1007/s00134-012-2684-z.

[31]

D. Liu and J. Du, A moving morphable components based shape reconstruction framework for electrical impedance tomography, IEEE Trans. Med. Imaging, 38 (2019), 2937-2948.  doi: 10.1109/TMI.2019.2918566.

[32]

D. Liu, V. Kolehmainen, S. Siltanen, A.-M. Laukkanen and A. Seppänen, Nonlinear difference imaging approach to three-dimensional electrical impedance tomography in the presence of geometric modeling errors, IEEE Trans. Biomedical Engineering, 63 (2016), 1956-1965.  doi: 10.1109/TBME.2015.2509508.

[33]

D. Liu, D. Smyl, D. Gu and J. Du, Shape-driven difference electrical impedance tomography, IEEE Trans. Med. Imaging, 39 (2020), 3801-3812.  doi: 10.1109/TMI.2020.3004806.

[34]

S. Liu, R. Cao, Y. Huang, T. Ouypornkochagorn and J. Jia, Time sequence learning for electrical impedance tomography using bayesian spatiotemporal priors, IEEE Trans. Instrumentation and Measurement, 69 (2020), 6045-6057.  doi: 10.1109/TIM.2020.2972172.

[35]

S. Liu, J. Jia, Y. D. Zhang and Y. Yang, Image reconstruction in electrical impedance tomography based on structure-aware sparse bayesian learning, IEEE Trans. Med. Imaging, 37 (2018), 2090-2102.  doi: 10.1109/TMI.2018.2816739.

[36]

S. Liu, J. Jia, Y. D. Zhang and Y. Yang, Image reconstruction in electrical impedance tomography based on structure-aware sparse bayesian learning, IEEE Trans. Med. Imaging, 37 (2018), 2090-2102.  doi: 10.1109/TMI.2018.2816739.

[37]

A. Lyckegaard, G. Johnson and P. Tafforeau, Correction of ring artifacts in X-ray tomographic images, Int. J. Tomo. Stat, 18 (2011), 1-9. 

[38]

S. Martin and C. T. M. Choi, A post-processing method for three-dimensional electrical impedance tomography, Scientific Reports, 7 (2017). doi: 10.1038/s41598-017-07727-2.

[39]

T. Mauri, A. Mercat and G. Grasselli, What's new in electrical impedance tomography, Intensive Care Medicine, 45 (2019), 674-677.  doi: 10.1007/s00134-018-5398-z.

[40]

M. M. Mellenthin et al., The ace1 electrical impedance tomography system for thoracic imaging, IEEE Tran. Instrumentation and Measurement, 68 (2019), 3137-3150. 

[41]

J. L. Mueller and S. Siltanen, Linear and Nonlinear Inverse Problems with Practical Applications, Computational Science & Engineering, 10. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2012. doi: 10.1137/1.9781611972344.

[42]

P. A. Muller, J. L. Mueller and M. M. Mellenthin, Real-time implementation of calderón's method on subject-specific domains, IEEE Tran. Medical Imaging, 36 (2017), 1868-1875. 

[43]

E. K. Murphy and J. L. Mueller, Effect of domain shape modeling and measurement errors on the 2-d d-bar method for eit, IEEE Tran. Med. Imaging, 28 (2009), 1576-1584.  doi: 10.1109/TMI.2009.2021611.

[44]

A. I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. Math., 143 (1996), 71-96.  doi: 10.2307/2118653.

[45]

S. Oh, T. Tang and R. Sadleir, Quantitative analysis of shape change in electrical impedance tomography (EIT), In 13th International Conference on Electrical Bioimpedance and the 8th Conference on Electrical Impedance Tomography, (2007), 424–427. doi: 10.1007/978-3-540-73841-1_110.

[46]

L. Pinhu, T. Whitehead, T. Evans and M. Griffiths, Ventilator-associated lung injury, The Lancet, 361 (2003), 332-340.  doi: 10.1016/S0140-6736(03)12329-X.

[47]

F. Sadi, S. Y. Lee and M. K. Hasan, Removal of ring artifacts in computed tomographic imaging using iterative center weighted median filter, Computers in Biology and Medicine, 40 (2010), 109-118.  doi: 10.1016/j.compbiomed.2009.11.007.

[48]

R. J. Sadleir and R. A. Fox, Detection and quantification of intraperitoneal fluid using electrical impedance tomography, IEEE Tran. Biomedical Engineering, 48 (2001), 484-491.  doi: 10.1109/10.915715.

[49]

S. Siltanen, J. Mueller and D. Isaacson, An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem, Inverse Probl., 16 (2000), 681-699.  doi: 10.1088/0266-5611/16/3/310.

[50]

N. K. Soni, H. Dehghani, A. Hartov and K. D. Paulsen, A novel data calibration scheme for electrical impedance tomography, Physiological Measurement, 24 (2003), 421-435.  doi: 10.1088/0967-3334/24/2/354.

[51]

N. K. Soni, A. Hartov, C. Kogel, S. P. Poplack and K. D. Paulsen, Multi-frequency electrical impedance tomography of the breast: New clinical results, Physiological Measurement, 25 (2004), 301-314.  doi: 10.1088/0967-3334/25/1/034.

[52]

E. Techner, M. Imhoff and S. Leonhardt, Electrical impedance tomography: Electrical impedance tomography: The realisation of regional ventilation monitoring, 2$^nd$ edition, 2015. https://www.draeger.com/Library/Content/EIT-Mini-Manual.pdf

[53]

V. Tomicic and R. Cornejo, Lung monitoring with electrical impedance tomography: Technical considerations and clinical applications, J. Thoracic Disease, 11 (2019), 3122-3155.  doi: 10.21037/jtd.2019.06.27.

[54]

S. Vergnole, G. Lamouche and M. L. Dufour, Artifact removal in fourier-domain optical coherence tomography with a piezoelectric fiber stretcher, Optics Letters, 33 (2008), 732-734.  doi: 10.1364/OL.33.000732.

[55]

T. Vu, M. Li, H. Humayun, Y. Zhou and J. Yao, A generative adversarial network for artifact removal in photoacoustic computed tomography with a linear-array transducer, Experimental Biology and Medicine, 245 (2020), 597-605.  doi: 10.1177/1535370220914285.

[56]

Z. Wang, A. Bovik, H. Sheikh and E. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Tran. Image Processing, 13 (2004), 600-612.  doi: 10.1109/TIP.2003.819861.

[57]

Y. Wu, B. Chen, K. Liu, C. Zhu, H. Pan, J. Jia, H. Wu and J. Yao, Shape reconstruction with multiphase conductivity for electrical impedance tomography using improved convolutional neural network method, IEEE Sensors Journal, 21 (2021), 9277-9287. 

[58]

G. Zhang et al., An on-line processing strategy for head movement interferences removal of dynamic brain electrical impedance tomography based on wavelet decomposition, Biomedical Engineering Online, 18 (2019).

[59]

Q. Zhang et al., Projection artifact removal improves visualization and quantitation of macular neovascularization imaged by optical coherence tomography angiography, Ophthalmology Retina, 1 (2017), 124-136. 

[60]

X. Zhang, J. Wang and L. Xing, Metal artifact reduction in x-ray computed tomography (CT) by constrained optimization, Medical Physics, 38 (2011), 701-711.  doi: 10.1118/1.3533711.

Figure 1.  Top row: a sample difference reconstruction $ \sigma $ (left) of one frame from Human Dataset 1, reconstructed with no priors, and the corresponding segmented lung region (right) compared against the lung region extracted from CT data, which we take to be ground truth. Note the large conductive artifacts on the left and right sides of the reconstruction (indicated by arrows) which distort the lung boundary. Bottom row: the reconstruction $ \sigma' $ which now includes a priori data, and corresponding segmented lung boundaries, showing improved sharpness of organ boundaries, but still exhibiting large artifacts
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  A flowchart illustrating the main steps of the proposed algorithm. Fourier data is represented by colored regions plotted in the (real or imaginary) $ k $-plane, with the origin at the center. The sets $ \mathcal{R}_1^{{ \mbox{Re}}} $ and $ \mathcal{R}_1^{{ \mbox{Im}}} $ are denoted by the general notation $ \mathcal{R}_1 $
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  Sample sequence of left and right artifact boundaries corresponding to each of 5 total iterations of Brown linear temporal smoothing, plotted on the same axes. The original extracted artifact boundaries are plotted in lightest gray, with subsequent iterations plotted in incrementally darker grayscale. The final artifact boundaries are plotted boldly, in black.
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4.  Original a priori boundaries with no artifacts (left), the reconstruction $ \sigma $ containing artifacts (center), and the modified boundaries which now include automatically extracted artifacts (right), for a sample frame from Human Dataset 1
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5.  Top row: Conductivity phantoms for Simulated Datasets A, B, and C, with added artifacts, used to generate simulated data. Bottom row: the corresponding phantoms with no artifacts, considered ground truth for quantitative validation purposes. The conductivity values used in the forward solution were $ \sigma_{\mathrm{heart}} = 0.75, \sigma_{\mathrm{lungs}} = 0.25, \sigma_{\mathrm{artifacts}} = 0.9, \sigma_{\mathrm{background}} = 0.5 $ S/m.
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6.  FEM meshes for Simulated Datasets A, B, and C, with added artifacts. Electrode centers are plotted using dots on the boundary
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 7.  Results from simulated data. Normalized reconstructions $ \sigma $ (no priors or artifact filtering, top row), $ \sigma' $ (with priors, no artifact filtering, center row), and $ \tilde\sigma' $ (with priors and artifact filtering, bottom row) corresponding to Simulated Datasets A, B, and C left to right as labeled. The appearance of induced lateral conductive artifacts in $ \sigma $ is not sufficiently improved by the addition of priors in $ \sigma' $. The reconstructions $ \tilde \sigma' $ exhibit visually reduced artifact appearance by comparison
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 8.  Results from simulated data. NRMSE values (top row) and SSIM values (bottom row) for Simulated Datasets A, B, and C as labeled, comparing normalized reconstructions $ \sigma' $ (with priors but no artifact filtering, solid blue bars) and $ \tilde \sigma' $ (with artifact filtering, striped bars), computed for both the entire domain (left column) and the true lung region (right column) in each reconstruction. We take the normalized conductivity phantom without artifacts to be ground truth. Note that smaller NRMSE values and larger SSIM values are desirable
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 9.  Results from simulated data. Level set segmentation of lung boundaries for reconstructions (blue) against the true lung region used in the conductivity phantom (gray), for $ \sigma' $ (with priors but no artifact filtering, top row), and $ \tilde\sigma' $ (with artifact filtering, bottom row), corresponding to Simulated Datasets A, B, and C left to right as labeled. Lungs regions corresponding to filtered reconstructions $ \tilde\sigma' $ exhibit greater visual fidelity to the ground truth lung shape as compared to those corresponding to reconstructions $ \sigma' $
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 10.  Results from simulated data. NRMSE values for the segmented lung regions for Simulated Datasets A, B, and C as labeled, comparing binary images of lung regions segmented from $ \sigma' $ (with priors but no artifact filtering, solid green bars) and $ \tilde \sigma' $ (with artifact filtering, striped bars), computed over the entire domain for each reconstruction. We take the binary lung region used in the conductivity phantom without artifacts to be ground truth. Note that smaller NRMSE values are desirable
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 11.  Archival CT scans corresponding to Human Datasets 1 (left) and 2 (right), collected upon inspiration in the plane of the electrodes immediately following the EIT scans. We take these scans to be ground truth, and they were used to extract the a priori boundaries for each dataset. Images are displayed in DICOM orientation
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 12.  Results from human data. Sequence of representative difference images corresponding to one full breathing cycle from Human Datasets 1 (top) and 2 (bottom). For each dataset, the top row gives the standard regularized D-bar reconstructions $ \sigma' $ with a priori sharpening methods applied. Note the appearance of lateral conductive artifacts in the reconstructions $ \sigma' $, which have not been removed by inclusion of a priori data. The bottom row for each dataset gives reconstructions after artifact filtering, showing significant reduction of artifacts and improvement of lung boundary shapes
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 13.  Results from human data. Plots of the segmented lung regions for the representative reconstructions $ \sigma' $ and $ \tilde\sigma' $ for Human Datasets 1 (top) and 2 (bottom). In each image, the segmented lung region (blue) is plotted over the lung region extracted from the CT scan (gray). Lungs regions corresponding to filtered reconstructions $ \tilde\sigma' $ exhibit greater visual fidelity to the ground truth lung shape as compared to those corresponding to reconstructions $ \sigma' $
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 14.  Results from human data. NRMSE values for the binary images of segmented lung regions corresponding to the representative reconstructions $ \sigma' $ (with priors, no artifact filtering, solid green), and $ \tilde\sigma' $ (with artifact filtering, striped) for Human Datasets 1 (top) and 2 (bottom) as compared to the lung region extracted from the CT scans for each patient, which we take to be ground truth. Smaller NRMSE values are desirable. This metric provides evidence that the reconstructions with artifact filtering exhibit greater fidelity to the ground truth lung shape
Figure Options

Download full-size image

Download as PowerPoint slide

[1]

Nuutti Hyvönen, Lassi Päivärinta, Janne P. Tamminen. Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps. Inverse Problems and Imaging, 2018, 12 (2) : 373-400. doi: 10.3934/ipi.2018017
[2]

Melody Dodd, Jennifer L. Mueller. A real-time D-bar algorithm for 2-D electrical impedance tomography data. Inverse Problems and Imaging, 2014, 8 (4) : 1013-1031. doi: 10.3934/ipi.2014.8.1013
[3]

Sarah Jane Hamilton, Andreas Hauptmann, Samuli Siltanen. A data-driven edge-preserving D-bar method for electrical impedance tomography. Inverse Problems and Imaging, 2014, 8 (4) : 1053-1072. doi: 10.3934/ipi.2014.8.1053
[4]

Melody Alsaker, Sarah Jane Hamilton, Andreas Hauptmann. A direct D-bar method for partial boundary data electrical impedance tomography with a priori information. Inverse Problems and Imaging, 2017, 11 (3) : 427-454. doi: 10.3934/ipi.2017020
[5]

Henrik Garde, Kim Knudsen. 3D reconstruction for partial data electrical impedance tomography using a sparsity prior. Conference Publications, 2015, 2015 (special) : 495-504. doi: 10.3934/proc.2015.0495
[6]

Ke Zhang, Maokun Li, Fan Yang, Shenheng Xu, Aria Abubakar. Electrical impedance tomography with multiplicative regularization. Inverse Problems and Imaging, 2019, 13 (6) : 1139-1159. doi: 10.3934/ipi.2019051
[7]

Bastian Gebauer. Localized potentials in electrical impedance tomography. Inverse Problems and Imaging, 2008, 2 (2) : 251-269. doi: 10.3934/ipi.2008.2.251
[8]

Sarah J. Hamilton, David Isaacson, Ville Kolehmainen, Peter A. Muller, Jussi Toivanen, Patrick F. Bray. 3D Electrical Impedance Tomography reconstructions from simulated electrode data using direct inversion $ \mathbf{t}^{\rm{{\textbf{exp}}}} $ and Calderón methods. Inverse Problems and Imaging, 2021, 15 (5) : 1135-1169. doi: 10.3934/ipi.2021032
[9]

Daniela Calvetti, Paul J. Hadwin, Janne M. J. Huttunen, Jari P. Kaipio, Erkki Somersalo. Artificial boundary conditions and domain truncation in electrical impedance tomography. Part II: Stochastic extension of the boundary map. Inverse Problems and Imaging, 2015, 9 (3) : 767-789. doi: 10.3934/ipi.2015.9.767
[10]

Daniela Calvetti, Paul J. Hadwin, Janne M. J. Huttunen, David Isaacson, Jari P. Kaipio, Debra McGivney, Erkki Somersalo, Joseph Volzer. Artificial boundary conditions and domain truncation in electrical impedance tomography. Part I: Theory and preliminary results. Inverse Problems and Imaging, 2015, 9 (3) : 749-766. doi: 10.3934/ipi.2015.9.749
[11]

Kari Astala, Jennifer L. Mueller, Lassi Päivärinta, Allan Perämäki, Samuli Siltanen. Direct electrical impedance tomography for nonsmooth conductivities. Inverse Problems and Imaging, 2011, 5 (3) : 531-549. doi: 10.3934/ipi.2011.5.531
[12]

Ville Kolehmainen, Matti Lassas, Petri Ola, Samuli Siltanen. Recovering boundary shape and conductivity in electrical impedance tomography. Inverse Problems and Imaging, 2013, 7 (1) : 217-242. doi: 10.3934/ipi.2013.7.217
[13]

Kim Knudsen, Matti Lassas, Jennifer L. Mueller, Samuli Siltanen. Regularized D-bar method for the inverse conductivity problem. Inverse Problems and Imaging, 2009, 3 (4) : 599-624. doi: 10.3934/ipi.2009.3.599
[14]

Dong liu, Ville Kolehmainen, Samuli Siltanen, Anne-maria Laukkanen, Aku Seppänen. Estimation of conductivity changes in a region of interest with electrical impedance tomography. Inverse Problems and Imaging, 2015, 9 (1) : 211-229. doi: 10.3934/ipi.2015.9.211
[15]

Liliana Borcea, Fernando Guevara Vasquez, Alexander V. Mamonov. Study of noise effects in electrical impedance tomography with resistor networks. Inverse Problems and Imaging, 2013, 7 (2) : 417-443. doi: 10.3934/ipi.2013.7.417
[16]

Gen Nakamura, Päivi Ronkanen, Samuli Siltanen, Kazumi Tanuma. Recovering conductivity at the boundary in three-dimensional electrical impedance tomography. Inverse Problems and Imaging, 2011, 5 (2) : 485-510. doi: 10.3934/ipi.2011.5.485
[17]

Nicolay M. Tanushev, Luminita Vese. A piecewise-constant binary model for electrical impedance tomography. Inverse Problems and Imaging, 2007, 1 (2) : 423-435. doi: 10.3934/ipi.2007.1.423
[18]

Erfang Ma. Integral formulation of the complete electrode model of electrical impedance tomography. Inverse Problems and Imaging, 2020, 14 (2) : 385-398. doi: 10.3934/ipi.2020017
[19]

Kimmo Karhunen, Aku Seppänen, Jari P. Kaipio. Adaptive meshing approach to identification of cracks with electrical impedance tomography. Inverse Problems and Imaging, 2014, 8 (1) : 127-148. doi: 10.3934/ipi.2014.8.127
[20]

Jérémi Dardé, Harri Hakula, Nuutti Hyvönen, Stratos Staboulis. Fine-tuning electrode information in electrical impedance tomography. Inverse Problems and Imaging, 2012, 6 (3) : 399-421. doi: 10.3934/ipi.2012.6.399

2021 Impact Factor: 1.483

Tools

Metrics

  • PDF downloads (382)
  • HTML views (328)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy