XIV Mediterranean Conference on Medical and Biological Engineering and Computing 2016 pp 1280-1284 | Cite as
EIT Imaging Regularization Based on Spectral Graph Wavelets
Abstract
Electrical Impedance Tomography (EIT) intends to reveal tissue conductivity distributions from measured electrical boundary conditions. This is an ill-posed inverse problem usually solved under the finite element method (FEM) framework. Wavelet transforms (WT) are used in many areas of medical imaging. To integrate wavelet techniques into the FEM framework, we view the finite element meshes as undirected graphs and introduce the spectral graph wavelet transform for regularization. Simulation results indicate that the spectral graph wavelet based regularization method produces smoother images than standard sparse regularization.
Keywords
Electrical Impedance Tomography Finite Element Method Spectral graph wavelet Inverse problemPreview
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References
- 1.Zhao, Z., et al., Regional ventilation in cystic fibrosis measured by electrical impedance tomography. J Cyst Fibros, 2012. 11(5): p. 412-8.Google Scholar
- 2.Zhao, Z., et al., Regional airway obstruction in cystic fibrosis determined by electrical impedance tomography in comparison with high resolution CT. Physiol Meas, 2013. 34(11): p. N107-14.Google Scholar
- 3.Dowrick, T., C. Blochet, and D. Holder, In vivo bioimpedance measurement of healthy and ischaemic rat brain: implications for stroke imaging using electrical impedance tomography. Physiol Meas, 2015. 36(6): p. 1273-82.Google Scholar
- 4.Holder, D.S., Electrical Impedance Tomography: Methods, History and Applications, Institute of Physics Institute of Physics Publishing, 2004: p. 3-64.Google Scholar
- 5.Leonhardt, S. and B. Lachmann, Electrical impedance tomography: the holy grail of ventilation and perfusion monitoring? Intensive Care Med, 2012. 38(12): p. 1917-29.Google Scholar
- 6.Javaherian, A., M. Soleimani, and K. Moeller, Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography. Physiol Meas, 2015. 36(1): p. 43-66.Google Scholar
- 7.M. Gehre, T.K., A. Lipponen, B. Jin, A. Seppänen, J. P. Kaipio and P. Maass, Sparsity reconstruction in electrical impedance tomography: An experimental evaluation. J. Comput. Appl. Math., 2012. 236: p. 2126–2136.Google Scholar
- 8.M. Gehre, T.K., C. Sebu and P. Maass, Sparse 3D reconstructions in electrical impedance tomography using real data. Inverse Probl. Sci. En., 2014. 22(1): p. 31-44.Google Scholar
- 9.David K. Hammonda, P.V., Rémi Gribonval, Wavelets on graphs via spectral graph theory. Applied and Computational Harmonic Analysis, 2011. 30(2): p. 129-150.Google Scholar
- 10.Brad Graham, A.A., A Nodal Jacobian Algorithm for Reduced Complexity EIT Reconstructions International Journal of Information and Systems Sciences, 2006. 2(4): p. 453-468.Google Scholar
- 11.J P Kaipio, V.K., M Vauhkonen and E Somersalo, Inverse problems with structural prior information, Inverse Problems. Inverse problems, 1999. 15(4): p. 713–729.Google Scholar
- 12.Adler, A. and W.R. Lionheart, Uses and abuses of EIDORS: an extensible software base for EIT. Physiol Meas, 2006. 27(5): p. S25-42.Google Scholar
- 13.Kondor, A.S.a.R., Kernels and regularization on graphs. In The Sixteenth Annual Conference on Learning Theory/The Seventh Workshop on Kernel Machines, 2003.Google Scholar
- 14.V. Ozolins, R.L., R. Caflisch and S. Osher, Compressed modes for variational problems in mathematics and physics. Proceedings of the National Academy of Sciences, 2013. 110(46): p. 18368–18373.Google Scholar
- 15.Maggioni, R.R.C.a.M., Diffusion wavelets. Appl. Comp. Harm. Anal., 2006. 21(1): p. 53-94.Google Scholar
- 16.Maggioni, R.R.C.a.M., Multiscale data analysis with diffusion wavelets,. Proc. SIAM Bioinf. Workshop, Minneapolis, 2007.Google Scholar
- 17.W.Yin, S.O., D.Goldfarb, and J. Darbon, Bregman iterative algorithms for compressed sensing and related problems. SIAM J. Imaging Sciences, 2008. 1(1): p. 143–168.Google Scholar
- 18.S. Osher, Y.M., B. Dong and W. Yin, Fast Linearized Bregman Iteration for Compressive Sensing and Sparse Denoising. Communications in Mathematical Sciences, 2010. 8(1): p. 93-111.Google Scholar
- 19.J.-L. Starck, F.M.a.J.F., Sparse image and signal processing : wavelets, curvelets, morphological diversity. 2010: Cambridge University Press.Google Scholar