Carr-Purcell-Meiboom-Gill (CPMG) is generally used as the measurement sequence of unilateral NMR (UMR) sensors, and the NMR signals collected by the sequence are composed of a series of echo signals. In the traditional CPMG measurement signal, each echo peak value is first taken and then denoised, which would lead to the inaccuracy of the peak point taken, resulting in deviation. To ensure the measurement result more accurate, this paper proposes to employ wavelet technology to denoise the echo signal first, and then take the peak point to analyze the data. Firstly, a simplified model of the spin-echo signal without the influence of gradient magnetic field was established, and white noise was applied to a certain extent. Then, Signal to Noise Ratio (SNR) and Root Mean Square Error (RMSE) were used as evaluation indexes. The denoising effects under different wavelet bases and thresholds were compared. Finally, the Matlab simulation result showed that wavelet analysis had a good effect on the denoising of unilateral NMR spin echo signal.
"Wavelet Denoising of Echo Signal of Unilateral Magnetic Resonance Sensor," Progress In Electromagnetics Research M,
Vol. 110, 25-38, 2022. doi:10.2528/PIERM22020801
1. Blumich, B., J. Perlo, and F. Casanova, "Mobile single-sided NMR," Progress in Nuclear Magnetic Resonance Spectroscopy, Vol. 52, 197-269, 2008. doi:10.1016/j.pnmrs.2007.10.002
2. Goga, N. O., et al., "Mobile NMR: Applications to materials and biomedicine," Journal of Optoelectronics and Advanced Materials, Vol. 8, No. 4, 1430, 2006.
3. Blümich, B., et al., "Advances of unilateral mobile NMR in nondestructive materials testing," Magnetic Resonance Imaging, Vol. 23, No. 2, 197-201, 2005. doi:10.1016/j.mri.2004.11.058
4. Blümich, B., "Applications in biology and medicine," Single-Sided NMR, 187-202, Springer, Berlin, Heidelberg, 2011.
5. Xia, Y., Z. Xu, J. Huang, J. Lin, and D. Yu, "Unilateral mini NMR sensor used for assessing the aging status of the sheds of composite insulators," Progress In Electromagnetics Research M, Vol. 42, 145-152, 2015. doi:10.2528/PIERM15040902
6. Xu, Z., et al., "Portable unilateral NMR measuring system for assessing the aging status of silicon rubber insulators," Applied Magnetic Resonance, Vol. 50, No. 1, 277-291, 2019. doi:10.1007/s00723-018-1061-7
7. Abragam, A., Principles of Nuclear Magnetism, Oxford University Press, Oxford, 1983.
8. Hansen, P. C., "Analysis of discrete ill-posed problems by means of the L-curve," SIAM Review, Vol. 34, No. 4, 561-580, 1992. doi:10.1137/1034115
9. Ross, M. M. B., G. R. Wilbur, P. F. de J. Cano Barrita, and B. J. Balcom, "A portable, submersible, MR sensor - The Proteus magnet," Journal of Magnetic Resonance, Vol. 326, 1-8, 2021.
10. Guoxing, X. and L. Liben, Principles of Nuclear Magnetic Resonance Imaging (in Chinese), Science Press, 2007.
11. Wang, F., et al., "Application of improved wavelet denoising method in GPS attitude determination," Journal of Astronautics, Vol. 29, No. 4, 1267-1271, 2008.
12. Gao, Z., et al., "Physicochemical characteristics of fly ashes and situation & prospect of its utilization as resources," Journal of Capital Normal University, Vol. 24, No. 1, 50-54, 2003.
13. Mohan, J., V. Krishnaveni, and Y. Guo, "A survey on the magnetic resonance image denoising methods," Biomedical Signal Processing and Control, Vol. 9, 56-69, 2014. doi:10.1016/j.bspc.2013.10.007
14. Gerig, G. and O. Kubler, "Nonlinear anisotropic filtering of MRI data," IEEE Transactions on Medical Imaging, Vol. 11, No. 2, 221-232, 1992. doi:10.1109/42.141646
15. Krissian, K. and S. Aja-Fernandez, "Noise-driven anisotropic diffusion ltering of MRI," IEEE Transactions on Image Processing, Vol. 18, No. 10, 2265, A Publication of the IEEE Signal Processing Society, 2009. doi:10.1109/TIP.2009.2025553
16. Pizurica, A., W. Philips, I. Lemahieu, and M. Acheroy, "A versatile wavelet domain noise filtration technique for medical imaging," IEEE Transactions on Medical Imaging, Vol. 22, 323-331, 2003. doi:10.1109/TMI.2003.809588
17. Muresan, D. D. and T. W. Parks, "Adaptive principal components and image denoising," IEEE International Conference on Image Process, Vol. 1, 101-104, 2003.
18. Yaroslavsky, L. P., K. Egiazarian, and J. Astola, "Transform domain image restoration methods: Review, comparison and interpretation," Nonlinear Image Processing and Pattern Analysis XII, Vol. 4304, 155-169, 2000.
19. Awate, S. P. and R. T. Whitaker, "Nonparametric neighborhood statistics for MRI denoising," International Conference on Information Processing in Medical Imaging, Springer-Verlag, 2005.
20. Manjón, J. V., P. Coupé, A. Buades, D. Louis Collins, and M. Robles, "New methods for MRI denoising based on sparseness and self-similarity," Medical Image Analysis, Vol. 16, No. 1, 18-27, 2012. doi:10.1016/j.media.2011.04.003
21. Zhang, K., et al., "Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising," IEEE Transactions on Image Processing, Vol. 26, No. 7, 3142-3155, 2016. doi:10.1109/TIP.2017.2662206
22. Jiang, D., et al., "Denoising of 3D magnetic resonance images with multi-channel residual learning of convolutional neural network," Japanese Journal of Radiology, Vol. 36, 566-574, 2018. doi:10.1007/s11604-018-0758-8
23. Gang, C., "Research on the application of MRI image denoising methods (in Chinese)," The Medical Forum, 2019.
25. Coifman, R. R., Y. Meyer, and V. Wickerhauser, "Wavelet analysis and signal processing," Wavelets and Their Applications, 1992.
26. Walnut, D. F., An Introduction to Wavelet Analysis, Springer Science & Business Media, 2002.
27. Mingcai, L., Wavelet Analysis and Its Applications, 1, Tsinghua University Press, Beijing, 2005.
28. Pan, G., "Research on key technology and applications of portable and fully open magnetic resonance instrument,", Chongqing University, 2015.
29. Tang, L. W. and D. F. Tang, "Wavelet signal denoising technique based on matlab," Journal of Hunan University of Science & Technology, Vol. 29, No. 1, 85-87, 2014.
30. O'Reilly, T. and A. G. Webb, "In vivo T1 and T2 relaxation time maps of brain tissue, skeletal muscle, and lipid measured in healthy volunteers at 50 mT," Magnetic Resonance in Medicine, Vol. 87, No. 2, 884-895, 2022. doi:10.1002/mrm.29009