volume | PIER Journals

Abstract

Electrical impedance tomography (EIT) is a technique for reconstructing conductivity distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. Sparse reconstruction can effectively reduce the noise and artifacts of reconstructed images and maintain edge information. The effective selection of sparse dictionary is the key to accurate sparse reconstruction. The EIT image can be efficiently reconstructed with adaptive dictionary learning, which is an iterative reconstruction algorithm by alternating the process of image reconstruction and dictionary learning. However, image accuracy and convergence rate depend on the initial dictionary, which was not given full consideration in previous studies. This leads to the low accuracy of image reconstruction model. In this paper, Recursive Least Squares Dictionary Learning Algorithm (RLS-DLA) is used to learn the initial dictionary for dictionary learning of sparse EIT reconstruction. Both simulated and experimental results indicate that the improved dictionary learning method not only improves the quality of reconstruction but also accelerates the convergence.

1. Wang, Q., et al. "Reconstruction of EIT images via patch based sparse representation over learned dictionaries," Instrumentation & Measurement Technology Conference, IEEE, 2015.

2. Goharian, M., M. Soleimani, and G. R. Moran, "A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data," Progress In Electromagnetics Research, Vol. 94, 19-32, 2009.
doi:10.2528/PIER09052003

3. Vauhkonen, M., et al. "Tikhonov regularization and prior information in electrical impedance tomography," IEEE Transactions on Medical Imaging, Vol. 17, No. 2, 285-293, 1998.
doi:10.1109/42.700740

4. Oraintara, S., "A method for choosing the regularization parameter in generalized tikhonov regularized linear inverse problems," Int. Conf. Image Process, Vol. 1, 2000.

5. Tian, W., M. F. Ramli, W. Yang, and J. Sun, "Investigation of relaxation factor in landweber iterative algorithm for electrical capacitance tomography," 2017 IEEE International Conference on Imaging Systems and Techniques (IST), 1-6, Beijing, 2017.

6. Baloch, G. and H. Ozkaramanli, "Image denoising via correlation-based sparse representation," Signal, Image and Video Processing, 2017.

7. Quan, X., et al. "Image denoising based on adaptive over-complete sparse representation," Chinese Journal of Scientific Instrument, Vol. 30, No. 9, 1886-1890, 2009.

8. Elad, M. and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries," IEEE Transactions on Image Processing, Vol. 15, 3736-3745, 2006 (Pubitemid 44811686).
doi:10.1109/TIP.2006.881969

9. Rubinstein, R., et al. "Dictionaries for sparse representation modeling," Proceedings of the IEEE, Vol. 98, No. 6, 1045-1057, 2010.
doi:10.1109/JPROC.2010.2040551

10. Wang, J., et al. "Split Bregman iterative algorithm for sparse reconstruction of electrical impedance tomography," Signal Processing, Vol. 92, No. 12, 2952-2961, 2012.
doi:10.1016/j.sigpro.2012.05.027

11. Aharon, M., M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation," IEEE Transactions on Signal Processing, Vol. 54, No. 11, 4311-4322, 2006.
doi:10.1109/TSP.2006.881199

12. Engan, K., K. Skretting, and J. H. Husøy, "A family of iterative LS-based dictionary learning algorithms, ILS-DLA, for sparse signal representation," Digital Signal Processing, Vol. 17, 32-49, Jan. 2007.
doi:10.1016/j.dsp.2006.02.002

13. Mailhé, B., S. Lesage, R. Gribonval, and F. Bimbot, "Shift-invariant dictionary learning for sparse representations: Extending K-SVD," Proceedings of the 16th European Signal Processing Conference (EUSIPCO2008), Lausanne, Switzerland, Aug. 2008.

14. Mairal, J., F. Bach, J. Ponce, and G. Sapiro, "Online dictionary learning for sparse coding," ICML’09: Proceedings of the 26th Annual International Conference on Machine Learning, 689-696, ACM, New York, NY, USA, Jun. 2009.

15. Su, H., F. Xing, and L. Yang, "Robust cell detection of histopathological brain tumor images using sparse reconstruction and adaptive dictionary selection," IEEE Trans Med Imaging, Vol. 35, No. 6, 1575-1586, 2016.
doi:10.1109/TMI.2016.2520502

16. Jin, B., T. Khan, and P. Maass, "A reconstruction algorithm for electrical impedance tomography based on sparsity regularization," International Journal for Numerical Methods in Engineering, Vol. 89, No. 3, 337-353, 2012.
doi:10.1002/nme.3247

17. Gong, B., et al. "Sparse regularization for EIT reconstruction incorporating structural in formation derived from medical imaging," Physiological Measurement, Vol. 37, No. 6, 843-862, 2016.
doi:10.1088/0967-3334/37/6/843

18. Wang, Q., et al. "Patch based sparse reconstruction for electrical impedance tomography," Sensor Review, Vol. 37, No. 3, 2017.

19. Fan, W., et al. "Modified sparse regularization for electrical impedance tomography," Review of Scientific Instruments, Vol. 87, 2016.

20. Zhao, B., H. X. Wang, X. Y. Chen, X. L. Shi, and W. Q. Yang, "Linearized solution to electrical impedance tomography based on the Schur conjugate gradient method," Measurement Science and Technology, Vol. 18, No. 11, 3373-3383, 2007.
doi:10.1088/0957-0233/18/11/017

21. Skretting, K. and K. Engan, "Image compression using learned dictionaries by RLS-DLA and compared with K-SVD," IEEE International Conference on Acoustics, IEEE, 2011.

22. Press, H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, "Section 2.7.3. Noodbury Formula," Numerical Recipes: The Art of Scientific Computing, 3rd Edition, Camdridge University Press, New York, ISBN 978-0-521-88068-8, 2007.

23. Adler, A., et al. "GREIT: A unified approach to 2D linear EIT reconstruction of lung images," Physiological Measurement, Vol. 30, No. 6, S35-S55, 2009.
doi:10.1088/0967-3334/30/6/S03

24. Abubaker, A. and P. M. van den Berg, "Total variation as a multiplicative constraint for solving inverse problems," IEEE Transactions on Image Processing, A Publication of the IEEE Signal Processing Society, Vol. 10, No. 9, 0-1392, 2001.

Dr. Xiuyan Li

Dr. Jingwan Zhang

Professor Jianming Wang

Dr. Qi Wang

Dr. Xiaojie Duan