volume | PIER Journals

Abstract

As a noninvasive imaging technique for the interior of objects, Electrical Impedance Tomography (EIT) is widely used in many fields of biomedicine. Sparse reconstruction algorithms have made major breakthroughs in the field of image reconstruction in recent years. The K-SVD algorithm is an adaptive dictionary signal sparse representation algorithm, which could improve the reconstruction accuracy. However, the parameters in the K-SVD algorithm are fixed, which cannot match all the measurement data of EIT very well. Moreover, the K-SVD algorithm adopts a greedy algorithm in the sparse coding stage, which has high computational complexity. In this study, an electrical impedance sparse imaging method based on DK-SVD (deep k-singular value decomposition) was designed. It provides the corresponding optimal model parameters for each set of measurement data through the method of multi-layer perceptron (MLP) network training, thereby improving the imaging quality. At the same time, the iterative soft threshold algorithm (ISTA) is used in the sparse coding stage to improve the convergence speed. The reconstruction results show that compared with the K-SVD algorithm and Total Variation (TV) algorithm, the reconstruction error of the DK-SVD method is smaller, and the irregular and sharp inclusions can be accurately reconstructed. Image artifacts are also greatly reduced.

1. Hong, S., K. Lee, U. Ha, H. Kim, Y. Lee, Y. Kim, and H.-J. Yoo, "A 4.9 mΩ-sensitivity mobile electrical impedance tomography IC for early breast-cancer detection system," IEEE Journal of Solid-State Circuits, Vol. 50, No. 1, 245-257, 2015.
doi:10.1109/JSSC.2014.2355835 Google Scholar

2. Fabrizi, L., A. McEwan, T. Oh, E. J. Woo, and D. S. Holder, "A comparison of two EIT systems suitable for imaging impedance changes in epilepsy," Physiological Measurement, Vol. 30, No. 6, S103-S120, 2009.
doi:10.1088/0967-3334/30/6/S07 Google Scholar

3. Nissinen, A., J. P. Kaipio, M. Vauhkonen, and V. Kolehmainen, "Contrast enhancement in EIT imaging of the brain," Physiological Measurement, Vol. 37, No. 1, 1-24, 2016.
doi:10.1088/0967-3334/37/1/1 Google Scholar

4. Jang, G. Y., G. Ayoub, Y. E. Kim, T. I. Oh, C. R. Chung, G. Y. Suh, and E. J. Woo, "Integrated EIT system for functional lung ventilation imaging," BioMedical Engineering OnLine, Vol. 18, No. 1, 1-18, 2019.
doi:10.1186/s12938-019-0701-y Google Scholar

5. Bradley, D. and J. Bagnell, "Differential sparse coding," Proc. Conf. Neural Information Processing Systems, 2008. Google Scholar

6. Wang, J., J. Yang, K. Yu, F. Lv, T. Huang, and Y. Gong, "Locality-constrained linear coding for image classification," 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 3360-3367, 2010. Google Scholar

7. Zylberberg, J., J. T. Murphy, and M. R. DeWeese, "A sparse codingmodel with synaptically local plasticity and spiking neurons can account for the diverse shapes of V1 simple cell receptivefields," PLOS Comput. Biol., Vol. 7, No. 10, e1002250, 2011.
doi:10.1371/journal.pcbi.1002250 Google Scholar

8. Davis, G., S. Mallat, and M. Avellaneda, "Adaptive greedy approximations," J. Construct. Approx., Vol. 13, 57-98, 1997.
doi:10.1007/BF02678430 Google Scholar

9. 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, Nov. 2006, doi: 10.1109/TSP.2006.881199.
doi:10.1109/TSP.2006.881199 Google Scholar

10. Yang, J., Y. Zhang, and W. Yin, "A fast alternating direction method for TVL1-L2 signal reconstruction from partial fourier data," IEEE Journal of Selected Topics in Signal Processing, Vol. 4, No. 2, 288-297, 2010.
doi:10.1109/JSTSP.2010.2042333 Google Scholar

11. Needell, D. and R. Vershynin, "Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit," IEEE Journal of Selected Topics in Signal Processing, Vol. 4, No. 2, 310-316, 2010.
doi:10.1109/JSTSP.2010.2042412 Google Scholar

12. Wang, Q., Z. Lian, J. Wang, Q. Chen, Y. Sun, X. Li, X. Duan, Z. Cui, and H. Wang, "Accelerated reconstruction of electrical impedance tomography images via patch based sparse representation," Review of Scientific Instruments, Vol. 87, No. 11, 114707, 2016.
doi:10.1063/1.4966998 Google Scholar

13. Wang, Q., P. Zhang, J. Wang, Q. Chen, Z. Lian, X. Li, Y. Sun, X. Duan, Z. Cui, B. Sun, and H.Wang, "Patch based sparse reconstruction for electrical impedance tomography," Sensor Review, Vol. 37, No. 3, 257-269, 2017.
doi:10.1108/SR-07-2016-0126 Google Scholar

14. Li, X., J. Zhang, J. Wang, Q. Wang, and X. Duan, "Recursive least squares dictionary learning algorithm for electrical impedance tomography," Progress In Electromagnetics Research C, Vol. 97, 151-162, 2019.
doi:10.2528/PIERC19081001 Google Scholar

15. Wang, C., D. Sun, and K. C. Toh, "Solving log-determinant optimization problems by a Newton-CG primal proximal point algorithm," Siam Journal on Optimization, Vol. 20, No. 6, 2994-3013, 2009.
doi:10.1137/090772514 Google Scholar

16. Hou, W. and Y. Mo, "Image reconstruction in electrical impedance tomography based on genetic algorithm," Shengwu Yixue Gongchengxue Zazhi/Journal of Biomedical Engineering, Vol. 20, No. 1, 107-110, 2003. Google Scholar

17. Marquina, A. and S. Osher, "Image super-resolution by TV-regularization and Bregman iteration," Journal of Scientific Computing, Vol. 37, No. 3, 367-382, 2008.
doi:10.1007/s10915-008-9214-8 Google Scholar

18. Yu, C., S. Fan, Y. Bo, and D. Chen, "A novel quasi-newton image reconstruction algorithm for electrical capacitance tomography system," 2009 ISECS International Colloquium on Computing, Communication, Control, and Management, 89-93, 2009.
doi:10.1109/CCCM.2009.5267974 Google Scholar

19. Dai, T. and A. Adler, "Electrical impedance tomography reconstruction using l₁ norms for data and image terms," 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2721-2724, 2008.
doi:10.1109/IEMBS.2008.4649764 Google Scholar

20. Gehre, M., T. Kluth, A. Lipponen, B. Jin, A. Seppänen, J. P. Kaipio, and P. Maassa, "Sparsity reconstruction in electrical impedance tomography: An experimental evaluation," Journal of Computational and Applied Mathematics, Vol. 236, No. 8, 2126-2136, 2012.
doi:10.1016/j.cam.2011.09.035 Google Scholar

21. Gehre, M., T. Kluth, C. Sebu, and P. Maass, "Sparse 3D reconstructions in electrical impedance tomography using real data," Inverse Problems in Science & Engineering, Vol. 22, No. 1, 31-44, 2014.
doi:10.1080/17415977.2013.827183 Google Scholar

22. Theertham, G. T., S. K. Varanasi, and P. Jampana, "Sparsity constrained reconstruction for electrical impedance tomography," IFAC-PapersOnLine, Vol. 53, No. 2, 355-360, 2020.
doi:10.1016/j.ifacol.2020.12.185 Google Scholar

23. Liu, S., R. Cao, Y. Huang, T. Ouypornkochagorn, and J. Jia, "Time sequence learning for electrical impedance tomography using bayesian spatiotemporal priors," IEEE Transactions on Instrumentation and Measurement, Vol. 69, No. 9, 6045-6057, 2020.
doi:10.1109/TIM.2020.2972172 Google Scholar

24. Shi, Y., Y. Wu, M. Wang, Z. Tian, X. Kong, and X. He, "Sparse image reconstruction of intracerebral hemorrhage with electrical impedance tomography," Journal of Medical Imaging, Vol. 8, No. 1, 014501, 2021.
doi:10.1117/1.JMI.8.1.014501 Google Scholar

25. Hu, G., J. Lin, G. Wang, and R. He, "Sparse reconstruction based channel estimation for underwater piezo-acoustic backscatter systems," 2021 IEEE 93rd Vehicular Technology Conference (VTC2021-Spring), 1-5, 2021. Google Scholar

26. Li, S., H. Wang, J. N. Chen, and Z. Cui, "An improved sparse reconstruction algorithm based on singular value decomposition for electrical resistance tomography," 2021 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 1-6, 2021. Google Scholar

27. Kou, S. and X. Feng, "Angle-micro-Doppler frequency image of underwater target multi-highlight combining with sparse reconstruction," Applied Acoustics, Vol. 188, 108563, 2022.
doi:10.1016/j.apacoust.2021.108563 Google Scholar

28. Donoho, D. L., "Compressed sensing," IEEE Trans. Inf. Theory, Vol. 52, 1289-1306, Apr. 2006.
doi:10.1109/TIT.2006.871582 Google Scholar

29. Ye, J. M., H. G. Wang, and W. Q. Yang, "Image reconstruction for electrical capacitance tomography based on sparse representation," IEEE Transactions on Instrumentation and Measurement, Vol. 64, No. 1, 89-102, Jan. 2015.
doi:10.1109/TIM.2014.2329738 Google Scholar

30. Jin, B., T. Khan, and P. Maass, "A reconstruction algorithm for electrical impedance tomography based on sparsity regularization," Int. J. Numer. Methods Eng., Vol. 89, 337-353, Jan. 2012.
doi:10.1002/nme.3247 Google Scholar

31. Qu, X. B., Y. Hou, F. Lam, D. Guo, J. H. Zhong, and Z. Chen, "Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator," Med. Image Anal., Vol. 18, 843-856, Aug. 2014.
doi:10.1016/j.media.2013.09.007 Google Scholar

32. Elad, M. and M. Aharon, "Image denoising via sparse and redundant representations over learned dictionaries," IEEE Trans. Image Process., Vol. 12, 3736-3745, 2006.
doi:10.1109/TIP.2006.881969 Google Scholar

33. Wang, Q., K. Sun, J. Wang, and R. Zhang, "Reconstruction of EIT images via patch based sparse representation over learned dictionaries," 2015 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings, 2044-2048, 2015.
doi:10.1109/I2MTC.2015.7151597 Google Scholar

34. Wang, M. and W. Yin, "Electrical impedance tomography,", US06940286B2, 2005. Google Scholar

35. Donoho, D. L. and M. Elad, "Optimally sparse representation in general (nonorthogonal) dictionaries via l₁ minimization," Proc. Nat. Acad. Sci. USA, Vol. 100, No. 5, 2197-2202, Mar. 2003.
doi:10.1073/pnas.0437847100 Google Scholar

36. Donoho, D. L., M. Elad, and V. N. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory, Vol. 52, No. 1, 6-18, Jan. 2006.
doi:10.1109/TIT.2005.860430 Google Scholar

37. Daubechies, I., M. Defrise, and C. D. Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math., Vol. 57, No. 11, 1413-1457, 2004.
doi:10.1002/cpa.20042 Google Scholar

38. Xiang, C., S. Ding, and T. H. Lee, "Geometrical interpretation and architecture selection of MLP," IEEE Transactions on Neural Networks, Vol. 16, No. 1, 84-96, 2005, doi:10.1109/tnn.2004.836197.
doi:10.1109/TNN.2004.836197 Google Scholar

39. Lacrama, D. L., V. Gherhes, F. Alexa, and T. M. Karnyanszky, "Automatic survey processing using a MLP neural net," 10th Symposium on Neural Network Applications in Electrical Engineering, 123-126, 2010.
doi:10.1109/NEUREL.2010.5644092 Google Scholar

Dr. Qi Wang

Dr. Xin Ding

Dr. Ming Ma

Dr. Xiuyan Li

Dr. Xiaojie Duan

Professor Jianming Wang