Research on Human Lung Impedance Tomography Based on Soft Thresholding Image Segmentation and Reduced-Order Tikhonov Regularization
Abstract
:1. Introduction
2. EIT Imaging Basic Principles
2.1. Mathematical Model of EIT Imaging
2.2. EIT Image Reconstruction
3. EIT Region of Interest Image Segmentation Methods
3.1. Maximum Entropy Threshold Image Segmentation Method
3.2. Soft-Threshold Region Segmentation Algorithm
4. Reduced-Order Tikhonov Regularization Imaging Based on Soft-Threshold Segmentation
- Firstly, an existing image reconstruction algorithm is used to obtain an initial distribution map g of the medium field, which serves as the initial image for subsequent image processing. The initial algorithm used in this study is the Tikhonov regularization algorithm.
- An image segmentation algorithm is used to segment the initial distribution map g into three parts: the inner region q1, the edge region q2, and the background region q3. The segmented medium distribution image is denoted as g*1.
- The background region is removed from the image reconstruction process to reduce the number of unknowns. The corresponding rows of the sensitivity matrix S are reduced based on the image segmentation result. The reduced sensitivity matrix is denoted as S*. The process of obtaining the reduced sensitivity matrix is shown as follows:
- Based on the obtained reduced sensitivity matrix S, the Tikhonov regularization imaging algorithm is applied to reconstruct the inner region q1 and the edge region q2. The reconstructed image after dimension reduction is denoted as .
- For the reconstructed image after dimension reduction, it is restored to the complete image based on the segmented medium distribution and the image segmentation result. The mathematical expression for the image restoration process is shown as follows:
- For the obtained complete reconstructed image , an image segmentation algorithm is applied once again to perform image segmentation and extract the regions of interest.
5. Numerical Simulation and Experimental Verification
5.1. Simulation Experimental Platform
5.2. Image Evaluation Metrics
- (1)
- Relative Error of Reconstructed Images (IRE)
- (2)
- Image Correlation Coefficient (ICC)
- (3)
- Structural Similarity Index (SSIM)
5.3. Numerical Simulation Verification
6. Experimental Validation
6.1. Experimental Platform Setup
6.2. Analysis of Experimental Results
7. Conclusions
- Post-processing of lung EIT reconstruction images using image segmentation algorithms allows for effective identification of regions of interest, resulting in clear and distinguishable human lung images with well-defined edges. However, this process may lead to some information loss. In terms of evaluation metrics, the use of image segmentation algorithms reduces the relative error (IRE) and improves the image correlation coefficient (ICC) of the reconstructed images, but it may decrease the structural similarity index (SSIM).
- Compared to fixed threshold segmentation methods, such as the maximum entropy threshold segmentation method, soft-threshold segmentation allows for adjusting the preservation degree of the edge region connected to the regions of interest and the background region. This widens the application scope of segmentation algorithms for EIT reconstruction by catering to different processing requirements.
- The reduced-order Tikhonov algorithm addresses the ill-posedness issue in EIT by excluding the partition points belonging to the background region from the sought grayscale vector. The combination of image segmentation algorithms and the reduced-order Tikhonov algorithm effectively enhances the ill-posedness issue in image reconstruction, resulting in higher-quality reconstructed images.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Serial No. | Abbreviation | Full Name of the Algorithm |
---|---|---|
1 | LBP | Linear back projection algorithm |
2 | Landweber | Landweber iterative imaging algorithm |
3 | Tikhonov | Tikhonov regularization algorithm |
4 | METS | Maximum entropy threshold segmentation algorithm |
5 | STS | Soft-threshold segmentation algorithm |
6 | RO-TK | Reduced-order Tikhonov regularization algorithm |
7 | STS-RO-TK | Segmentation-reduced-order Tikhonov regularization algorithm |
8 | STS-RO-STS-TK | Segmentation-reduced-order-segmentation Tikhonov regularization algorithm |
References
- Krick, S.; Geraghty, P.; Jourdan Le Saux, C.; Rojas, M.; Staab-Weijnitz, C.A. Defining and Characterizing Respiratory Disease in an Aging Population. Front. Med. 2022, 9, 889834. [Google Scholar] [CrossRef] [PubMed]
- Zhang, Y.; Wang, Z.; Cao, Y.; Zhang, L.; Wang, G.; Dong, F.; Deng, R.; Guo, B.; Zeng, L.; Wang, P.; et al. The Effect of Consecutive Ambient Air Pollution on the Hospital Admission from Chronic Obstructive Pulmonary Disease in the Chengdu Region, China. Air Qual. Atmos. Health 2021, 14, 1049–1061. [Google Scholar] [CrossRef] [PubMed]
- Shono, A.; Kotani, T.; Frerichs, I. Personalisation of Therapies in COVID-19 Associated Acute Respiratory Distress Syndrome, Using Electrical Impedance Tomography. J. Crit. Care Med. 2021, 7, 62–66. [Google Scholar] [CrossRef] [PubMed]
- Nakamura, H.; Hirai, T.; Kurosawa, H.; Hamada, K.; Matsunaga, K.; Shimizu, K.; Konno, S.; Muro, S.; Fukunaga, K.; Nakano, Y.; et al. Current Advances in Pulmonary Functional Imaging. Respir. Investig. 2024, 62, 49–65. [Google Scholar] [CrossRef] [PubMed]
- Shono, A.; Kotani, T. Clinical Implication of Monitoring Regional Ventilation Using Electrical Impedance Tomography. J. Intensive Care 2019, 7, 4. [Google Scholar] [CrossRef] [PubMed]
- Piraino, T. An Introduction to the Clinical Application and Interpretation of Electrical Impedance Tomography. Respir. Care 2022, 67, 721–729. [Google Scholar] [CrossRef] [PubMed]
- Sbarbaro, D.; Vauhkonen, M.; Johansen, T.A. State Estimation and Inverse Problems in Electrical Impedance Tomography: Observability, Convergence and Regularization. Inverse Probl. 2015, 31, 045004. [Google Scholar] [CrossRef]
- Ding, M.; Li, X.; Zhao, S. Application of Constrained Coefficient Fuzzy Linear Programming in Medical Electrical Impedance Tomography. Appl. Math. Sci. Eng. 2022, 30, 762–776. [Google Scholar] [CrossRef]
- Yan, H.; Wang, Y.; Wang, Y.; Zhou, Y. An ECT Image Reconstruction Algorithm Based on Object-and-Background Adaptive Regularization. Meas. Sci. Technol. 2021, 32, 015402. [Google Scholar] [CrossRef]
- Ko, Y.F.; Cheng, K.S. U-Net-Based Approach for Automatic Lung Segmentation in Electrical Impedance Tomography. Physiol. Meas. 2021, 42, 025002. [Google Scholar] [CrossRef]
- Song, X.; Xu, Y.; Dong, F. Linearized Image Reconstruction Method for Ultrasound Modulated Electrical Impedance Tomography Based on Power Density Distribution. Meas. Sci. Technol. 2017, 28, 045404. [Google Scholar] [CrossRef]
- Wang, J. A Two-step Accelerated Landweber-type Iteration Regularization Algorithm for Sparse Reconstruction of Electrical Impedance Tomography. Math. Methods Appl. Sci. 2021, 47, 3261–3272. [Google Scholar] [CrossRef]
- Wang, Z.; Liu, X. A Regularization Structure Based on Novel Iterative Penalty Term for Electrical Impedance Tomography. Measurement 2023, 209, 112472. [Google Scholar] [CrossRef]
- Xu, Y.; Pei, Y.; Dong, F. An Adaptive Tikhonov Regularization Parameter Choice Method for Electrical Resistance Tomography. Flow. Meas. Instrum. 2016, 50, 1–12. [Google Scholar] [CrossRef]
- Shi, Y.; Zhang, Y.; Wang, M.; Lou, Y.; Zheng, S. Reconstruction of Conductivity Distribution Variation with Tikhonov and Wavelet Frame Combined Method for Electrical Impedance Tomography. Trans. Inst. Meas. Control 2023, 45, 2658–2668. [Google Scholar] [CrossRef]
- Liu, S.; Cao, R.; Huang, Y.; Ouypornkochagorn, T.; Ji, J. Time Sequence Learning for Electrical Impedance Tomography Using Bayesian Spatiotemporal Priors. IEEE Trans. Instrum. Meas. 2020, 69, 6045–6057. [Google Scholar] [CrossRef]
- Chen, B.; Abascal, J.; Soleimani, M. Electrical Resistance Tomography for Visualization of Moving Objects Using a Spatiotemporal Total Variation Regularization Algorithm. Sensors 2018, 18, 1704. [Google Scholar] [CrossRef] [PubMed]
- Song, Y.; Wang, Y.; Liu, D. A Nonlinear Weighted Anisotropic Total Variation Regularization for Electrical Impedance Tomography. IEEE Trans. Instrum. Meas. 2022, 71, 1–13. [Google Scholar] [CrossRef]
- Gong, B.; Schullcke, B.; Krueger-Ziolek, S.; Zhang, F.; Mueller-Lisse, U.; Moeller, K. Higher Order Total Variation Regularization for EIT Reconstruction. Med. Biol. Eng. Comput. 2018, 56, 1367–1378. [Google Scholar] [CrossRef]
- Shi, Y.; Kong, X.; Wang, M.; Wu, Y.; Yang, L. A Non-Convex L1-Norm Penalty-Based Total Generalized Variation Model for Reconstruction of Conductivity Distribution. IEEE Sens. J. 2020, 20, 8137–8146. [Google Scholar] [CrossRef]
- Guo, Q.; Li, X.; Hou, B.; Mariethoz, G.; Ye, M.; Yang, W.; Liu, Z. A Novel Image Reconstruction Strategy for ECT: Combining Two Algorithms With a Graph Cut Method. IEEE Trans. Instrum. Meas. 2020, 69, 804–814. [Google Scholar] [CrossRef]
- Borgmann, S.; Linz, K.; Braun, C.; Dzierzawski, P.; Spassov, S.; Wenzel, C.; Schumann, S. Lung Area Estimation Using Functional Tidal Electrical Impedance Variation Images and Active Contouring. Physiol. Meas. 2022, 43, 075010. [Google Scholar] [CrossRef]
- Khambampati, A.K.; Liu, D.; Konki, S.K.; Kim, K.Y. An Automatic Detection of the ROI Using Otsu Thresholding in Nonlinear Difference EIT Imaging. IEEE Sens. J. 2018, 18, 5133–5142. [Google Scholar] [CrossRef]
- Arshad, S.H.; Murphy, E.K.; Halter, R.J. Automated Segmentation and Feature Extraction in Cardiac Electrical Impedance Tomography Images. In Progress in Biomedical Optics and Imaging, Proceedings of the Medical Imaging 2018: Biomedical Applications in Molecular, Structural, and Functional Imaging, Houston, TX, USA, 11–13 February 2018; Gimi, B., Krol, A., Eds.; SPIE: Bellingham, WA, USA, 2018; p. 61. [Google Scholar]
- Seo, J.K.; Lee, J.; Kim, S.W.; Zribi, H.; Woo, E.J. Frequency-difference electrical impedance tomography (fdEIT): Algorithm development and feasibility study. Physiol. Meas. 2008, 29, 929–944. [Google Scholar] [CrossRef] [PubMed]
- Gao, H.; Kang, W. Tikhonov Regularization Parameter Based on Augmented Lagrange Improves Photoacoustic Tomography. In Applications of Digital Image Processing XLIII; Tescher, A.G., Ebrahimi, T., Eds.; SPIE: Bellingham, WA, USA, 2020; p. 76. [Google Scholar]
- Zhu, P.; Ding, Y.; Gu, Y. Emery Particles Identification under Contour Extraction with Maximum Entropy Approaches. Int. J. Model. Identif. Control 2021, 38, 81. [Google Scholar] [CrossRef]
- Chandrasekar, K.S.; Geetha, P. Highly Efficient Neoteric Histogram–Entropy-based Rapid and Automatic Thresholding Method for Moving Vehicles and Pedestrians Detection. IET Image Process 2020, 14, 354–365. [Google Scholar] [CrossRef]
- Thapa, S.; Lukat, N.; Selhuber-Unkel, C.; Cherstvy, A.G.; Metzler, R. Transient superdiffusion of polydisperse vacuoles in highly motile amoeboid cells. J. Chem. Phys. 2019, 150, 144901. [Google Scholar] [CrossRef]
LBP | Landweber | Tikhonov | METS | STS | RO-TK | STS-RO-TK | STS-RO-STS-TK | |
---|---|---|---|---|---|---|---|---|
IRE | 0.9369 | 0.7024 | 0.7534 | 0.7273 | 0.6713 | 0.7275 | 0.6296 | 0.5683 |
ICC | 0.6018 | 0.8490 | 0.8061 | 0.8480 | 0.8839 | 0.8311 | 0.9128 | 0.9355 |
SSIM | 3.6395 | 6.7307 | 6.0299 | 5.4428 | 6.0037 | 6.3347 | 7.2632 | 7.1012 |
LBP | Landweber | Tikhonov | METS | STS | RO-TK | STS-RO-TK | STS-RO-STS-TK | |
---|---|---|---|---|---|---|---|---|
IRE | 1.0731 | 0.7373 | 0.8063 | 0.7360 | 0.6707 | 0.7463 | 0.6335 | 0.5390 |
ICC | 0.5048 | 0.8309 | 0.7748 | 0.8601 | 0.8936 | 0.8283 | 0.9160 | 0.9518 |
SSIM | 2.8678 | 8.8574 | 7.4348 | 7.3229 | 8.3938 | 8.5889 | 10.3124 | 10.1009 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Song, Y.; Xiong, L.; Liu, Z.; Wu, Y.; Zhang, Z. Research on Human Lung Impedance Tomography Based on Soft Thresholding Image Segmentation and Reduced-Order Tikhonov Regularization. Appl. Sci. 2024, 14, 3309. https://doi.org/10.3390/app14083309
Song Y, Xiong L, Liu Z, Wu Y, Zhang Z. Research on Human Lung Impedance Tomography Based on Soft Thresholding Image Segmentation and Reduced-Order Tikhonov Regularization. Applied Sciences. 2024; 14(8):3309. https://doi.org/10.3390/app14083309
Chicago/Turabian StyleSong, Yang, Lan Xiong, Zhenyou Liu, Yongye Wu, and Zhanlong Zhang. 2024. "Research on Human Lung Impedance Tomography Based on Soft Thresholding Image Segmentation and Reduced-Order Tikhonov Regularization" Applied Sciences 14, no. 8: 3309. https://doi.org/10.3390/app14083309