skip to main content
10.1145/3404716.3404722acmotherconferencesArticle/Chapter ViewAbstractPublication PagesicmsspConference Proceedingsconference-collections
research-article

Electrical Resistance Tomographic Image Enhancement Using MRNSD and LSQR

Published: 08 July 2020 Publication History

Abstract

Images in tomography are vital to control measurand in the process industry. Electrical resistance tomography (ERT) measure process variable by reconstruction conductivity distribution from the electrical boundary changes. The measured value leads towards a system of large ill-posed matrix that has more one possible solution. The digitalization of measurand, turn problem into an inverse problem. Various reconstruction algorithms (i.e., iterative techniques and transform-based methods) are present to solve these inverse problems. A few steepest descent Krylov solvers such as CGLS, CRLS, LSMR etc. are there to tackle ill-posed problems with some issue. Minimal residual norm steepest descent (MRNSD) and least square QR factorization (LSQR) are the steepest descent Krylov solvers to handle tomographic ill-posed problems in robust and intrusive manner. The semi-converge is the main issue for MRNSD and LSQR. An adequate stopping criterion to handle semi-convergence for these algorithms presented in this work. Moreover, this work performed in perspective of data received in electrical resistance tomographic system.

References

[1]
Sun, J. and Yang, W. 2015. A dual-modality electrical tomography sensor for measurement of gas-oil-water stratified flows. Measurements 66, (Apr. 2015), 150--160. DOI=https://doi.org/10.1016/j.measurement.2015.01.032.
[2]
Guo, G., Tong, G., Lu, L. and Liu, S. 2018. Iterative reconstruction algorithm for the inverse problems in electrical capacitance tomography. Flow Measurement and Instrumentation. 64, (Dec. 2018), 204--212. DOI= https://doi.org/10.1016/j.flowmeasinst.2018.10.010.
[3]
Engl, H.W., Rundell, W. and Scherzer, O. 1994. A Regularization Scheme for an Inverse Problem in Age-Structured Populations. Journal of Mathematical Analysis and Applications. 182, 3 (Mar. 1994), 658--679. DOI= https://doi.org/10.1006/JMAA. 1994.1112.
[4]
Lin, Y. and Simoncini, V. 2013. Minimal residual methods for large scale Lyapunov equations. Applied Numerical Mathematics. 72, (Oct. 2013), 52--71. DOI= https://doi.org/10.1016/j.apnum.2013.04.004.
[5]
Hnêtynková, I., Kubínová, M. and Plešinger, M. 2017. Noise representation in residuals of LSQR, LSMR, and CRAIG regularization. Linear Algebra and its Applications. 533, (Nov. 2017), 357--379. DOI= https://doi.org/10.1016/j.laa.2017.07.031.
[6]
De-Cezaro, A., Haltmeier, M., Leitão, A. and Scherzer, O. 2008. On Steepest-Descent-Kaczmarz methods for regularizing systems of nonlinear ill-posed equations. Applied Mathematics and Computation. 202, 2 (Aug. 2008), 596--607. DOI= https://doi.org/10.1016/j.amc.2008.03.010.
[7]
Calvetti, D., Reichel, L. and Shuibi, A. 2005. Invertible smoothing preconditioners for linear discrete ill-posed problems. Applied Numerical Mathematics. 54, 2 (Jul. 2005), 135--149. DOI= https://doi.org/10.1016/j.apnum.2004.09.027.
[8]
Lu, H., Guo, X., Jin, Y. and Gong, X. 2018. Effect of moisture on flowability of pulverized coal. Chemical Engineering Research and Design. 133, (2018), 326--334. DOI= https://doi.org/10.1016/j.cherd.2018.03.023.
[9]
Li, J., Fu, F., Li, S., Xu, C. and Wang, S. 2015. Velocity characterization of dense phase pneumatically conveyed solid particles in horizontal pipeline through an integrated electrostatic sensor. International Journal of Multiphase Flow. 76, (2015), 198--211. DOI= https://doi.org/10.1016/j.ijmultiphaseflow.2014.11.004.
[10]
Chen, Y., Zhang, Y., Zhang, K., Deng, Y., Wang, S., Zhang, F. and Sun, F. 2016. FIRT: Filtered iterative reconstruction technique with information restoration. Journal of Structural Biology. 195, 1 (Jul. 2016), 49--61. DOI= https://doi.org/10.1016/j.jsb.2016.04.015.
[11]
Jia, Y., Chernyshev, V. and Skliar, M. 2016. Ultrasound measurements of segmental temperature distribution in solids: Method and its high-temperature validation. Ultrasonics. 66, (Mar. 2016), 91--102. DOI= https://doi.org/10.1016/j.ultras.2015.11.006.
[12]
Ahmad, S.A, Taib, M.N., Abdul-Khalid, N.E. and Taib, H. 2012. An Analysis of Image Enhancement Techniques for Dental X-ray Image Interpretation. International Journal of Machine Learning and Computing. 2, 3 (Jun. 2012), 292--297. DOI= https://doi.org/ 10.7763/ijmlc.2012.V2.133.
[13]
Grudzień, K., Chaniecki, Z. and Babout, L. 2018. Study of granular flow in silo based on electrical capacitance tomography and optical imaging. Flow Measurement and Instrumentation. 62, (Aug. 2018), 186--195. DOI= https://doi.org/10.1016/j.flowmeasinst.2017.11.001.
[14]
Dyakowski, T., Edwards, R.B., Xie, C.G. and Williams, R.A. 1997. Application of capacitance tomography to gas-solid flows. Chemical Engineering Science. 52, 13 (1997), 2099--2110. DOI= https://doi.org/10.1016/S0009-2509(97)00037-7.
[15]
Yu-Ling Lai, Wen-Wei Lin and Pierce, D. 1997. Conjugate gradient and minimal residual methods for solving symmetric indefinite systems. Journal of Computational and Applied Mathematics. 84, 2 (Oct. 1997), 243--256. DOI= https://doi.org/10.1016/S0377-0427(97)00127-1.
[16]
Xu, Y., Pei, Y. and Dong, F. 2016. An adaptive Tikhonov regularization parameter choice method for electrical resistance tomography. Flow Measurement and Instrumentation. 50, (2016), 1--12. DOI= https://doi.org/10.1016/j.flowmeasinst.2016.05.004.
[17]
Ren, S., Zhao, J. and Dong, F. 2015. Dimensionality reduced simultaneous iterative reconstruction technique for electrical resistance tomography. Flow Measurement and Instrumentation. 46, (Dec. 2015), 284--291. DOI= https://doi.org/10.1016/j.flowmeasinst.2015.07.004.
[18]
Liu, C. 2012. Modifications of Steepest Descent Method and Conjugate Gradient Method Against Noise for Ill-posed Linear Systems. Communications in Numerical Analysis. 20 (2012), 1--24. DOI= https://doi.org/10.5899/2012/cna-00115.
[19]
Huang, J., Huang, T.Z., Zhao, X. Le, Xu, Z. Ben and Lv, X.G. 2014. Two soft-thresholding based iterative algorithms for image deblurring. Information Sciences. 271, (2014), 179--195. DOI= https://doi.org/10.1016/j.ins.2014.02.089.
[20]
Sharifi, M. and Young, B. 2011. 3-Dimensional spatial monitoring of tanks for the milk processing industry using electrical resistance tomography. Journal of Food Engineering. 105, 2 (2011), 312--319. DOI= https://doi.org/10.1016/j.jfoodeng.2011.02.041.
[21]
Kotzé, R., Adler, A., Sutherland, A. and Deba, C.N. 2019. Evaluation of Electrical Resistance Tomography imaging algorithms to monitor settling slurry pipe flow. Flow Measurement and Instrumentation. 68, June (2019), 101572. DOI= https://doi.org/10.1016/j.flowmeasinst.2019.101572.

Cited By

View all
  • (2024)The Gaia AVU–GSR solver: CPU+GPU parallel solutions for linear systems solving and covariances calculation toward exascale systemsSoftware and Cyberinfrastructure for Astronomy VIII10.1117/12.3018102(61)Online publication date: 25-Jul-2024
  • (2024)Toward HPC application portability via C++ PSTL: the Gaia AVU-GSR code assessmentThe Journal of Supercomputing10.1007/s11227-024-06011-180:10(14369-14390)Online publication date: 19-Mar-2024
  • (2023)The MPI + CUDA Gaia AVU–GSR Parallel Solver Toward Next-generation Exascale InfrastructuresPublications of the Astronomical Society of the Pacific10.1088/1538-3873/acdf1e135:1049(074504)Online publication date: 1-Aug-2023

Index Terms

  1. Electrical Resistance Tomographic Image Enhancement Using MRNSD and LSQR

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Other conferences
    ICMSSP '20: Proceedings of the 2020 5th International Conference on Multimedia Systems and Signal Processing
    May 2020
    112 pages
    ISBN:9781450377485
    DOI:10.1145/3404716
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    In-Cooperation

    • Shenzhen University: Shenzhen University

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 08 July 2020

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. Electrical Resistance Tomography
    2. Iterative reconstruction
    3. LSQR
    4. MRNSD
    5. Steep-Descent
    6. Tomography

    Qualifiers

    • Research-article
    • Research
    • Refereed limited

    Conference

    ICMSSP 2020

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)13
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 17 Feb 2025

    Other Metrics

    Citations

    Cited By

    View all
    • (2024)The Gaia AVU–GSR solver: CPU+GPU parallel solutions for linear systems solving and covariances calculation toward exascale systemsSoftware and Cyberinfrastructure for Astronomy VIII10.1117/12.3018102(61)Online publication date: 25-Jul-2024
    • (2024)Toward HPC application portability via C++ PSTL: the Gaia AVU-GSR code assessmentThe Journal of Supercomputing10.1007/s11227-024-06011-180:10(14369-14390)Online publication date: 19-Mar-2024
    • (2023)The MPI + CUDA Gaia AVU–GSR Parallel Solver Toward Next-generation Exascale InfrastructuresPublications of the Astronomical Society of the Pacific10.1088/1538-3873/acdf1e135:1049(074504)Online publication date: 1-Aug-2023
    • (2022)The Gaia AVU–GSR parallel solver: Preliminary studies of a LSQR-based application in perspective of exascale systemsAstronomy and Computing10.1016/j.ascom.2022.10066041(100660)Online publication date: Oct-2022

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Figures

    Tables

    Media

    Share

    Share

    Share this Publication link

    Share on social media