{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T02:22:59Z","timestamp":1775787779277,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2009,12,18]],"date-time":"2009-12-18T00:00:00Z","timestamp":1261094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Electrical charge tomography (EChT) is a non-invasive imaging technique that is aimed to reconstruct the image of materials being conveyed based on data measured by an electrodynamics sensor installed around the pipe. Image reconstruction in electrical charge tomography is vital and has not been widely studied before. Three methods have been introduced before, namely the linear back projection method, the filtered back projection method and the least square method. These methods normally face ill-posed problems and their solutions are unstable and inaccurate. In order to ensure the stability and accuracy, a special solution should be applied to obtain a meaningful image reconstruction result. In this paper, a new image reconstruction method \u2013 Least squares with regularization (LSR) will be introduced to reconstruct the image of material in a gravity mode conveyor pipeline for electrical charge tomography. Numerical analysis results based on simulation data indicated that this algorithm efficiently overcomes the numerical instability. The results show that the accuracy of the reconstruction images obtained using the proposed algorithm was enhanced and similar to the image captured by a CCD Camera. As a result, an efficient method for electrical charge tomography image qreconstruction has been introduced.<\/jats:p>","DOI":"10.3390\/s91210291","type":"journal-article","created":{"date-parts":[[2009,12,18]],"date-time":"2009-12-18T12:47:28Z","timestamp":1261140448000},"page":"10291-10308","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Electrodynamics Sensor for the Image Reconstruction Process in an Electrical Charge Tomography System"],"prefix":"10.3390","volume":"9","author":[{"given":"Mohd Fua\u2019ad","family":"Rahmat","sequence":"first","affiliation":[{"name":"Control and Instrumentation Engineering Department, Faculty of Electrical Engineering, Universiti Technologi Malaysia, 81310 Skudai, Johor Bharu, Johor, Malaysia"}]},{"given":"Mohd Daud","family":"Isa","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Politeknik Kota Bharu, KM.24 Kok Lanas, 16400 Ketereh, Kota Bharu, Kelantan, Malaysia"}]},{"given":"Ruzairi Abdul","family":"Rahim","sequence":"additional","affiliation":[{"name":"Control and Instrumentation Engineering Department, Faculty of Electrical Engineering, Universiti Technologi Malaysia, 81310 Skudai, Johor Bharu, Johor, Malaysia"}]},{"given":"Tengku Ahmad Raja","family":"Hussin","sequence":"additional","affiliation":[{"name":"Department of General Studies, Politeknik Kota Bharu, KM.24 Kok Lanas, 16400 Ketereh, Kota Bharu, Kelantan, Malaysia"}]}],"member":"1968","published-online":{"date-parts":[[2009,12,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/S0955-5986(00)00023-6","article-title":"Role of tomography in gas\/solids flow measurement","volume":"11","author":"Yang","year":"2000","journal-title":"Flow Measur. Instrum."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.flowmeasinst.2008.04.001","article-title":"An Image reconstruction algorithm based on the regularization total least squares method for electrical capacitance tomography","volume":"19","author":"Lei","year":"2008","journal-title":"Flow Meas. Instrum."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0957-0233\/14\/1\/201","article-title":"Review article: image reconstruction algorithms for electrical capacitance tomography","volume":"14","author":"Yang","year":"2003","journal-title":"Meas. Sci. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1002\/1521-4117(200010)17:3<96::AID-PPSC96>3.0.CO;2-8","article-title":"Using regularization methods for image reconstruction of electrical capacitance tomography","volume":"17","author":"Peng","year":"2000","journal-title":"Part. Part. Syst. Character."},{"key":"ref_5","unstructured":"Lionheart, W.R.B. Reconstruction algorithms for permittivity and conductivity imaging. Hannover, Germany."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1088\/0266-5611\/4\/3\/004","article-title":"Linear inverse problem with discrete data: ii stability and regularization inverse problem","volume":"4","author":"Bertero","year":"1988","journal-title":"Inverse Probl."},{"key":"ref_7","first-page":"561","article-title":"Analysis of Discrete Ill-Posed Problem by means of L-Curve","volume":"4","author":"Hansen","year":"1992","journal-title":"Soc. Industr. Appl. Mathem. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation, Society for Industrial and Applied Mathematics (SIAM).","DOI":"10.1137\/1.9780898717921"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1137\/0914086","article-title":"The use of the L-curve in the regularization of discrete ill-posed problems","volume":"14","author":"Hansen","year":"1993","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1088\/0957-0233\/14\/7\/327","article-title":"On-line particle sizing of pulverized and granular fuels using digital imaging techniques","volume":"14","author":"Carter","year":"2003","journal-title":"Meas. Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0021-8502(96)00175-9","article-title":"Mathematical model for charged particle measurement","volume":"27","author":"Machida","year":"1996","journal-title":"J. Aerosol Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1088\/0957-0233\/6\/5\/013","article-title":"Velocity measurement of pneumatically conveyed solids using electrodynamics sensors","volume":"6","author":"Yan","year":"1995","journal-title":"Meas. Sci. Technol."},{"key":"ref_13","first-page":"200","article-title":"An electrodynamics sensor for electrostatic charge measurement","volume":"2","author":"Rahmat","year":"2009","journal-title":"Int. J. Smart Sen. Intell. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1088\/0957-0233\/8\/2\/014","article-title":"Concentration profiles of dry powders in a gravity conveyor using an electrodynamics tomography system","volume":"8","author":"Rahmat","year":"1997","journal-title":"Meas. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/BF03182206","article-title":"Sensor design for development of tribo-electric tomography system with increased number of sensors","volume":"11","author":"Machida","year":"2008","journal-title":"J. Vis."},{"key":"ref_16","unstructured":"Isa, M.D., and Rahmat, M.F. (, January November). Image reconstruction algorithm based on least square with regularization for process tomography system using electrical charge carried by particles. Johor, Malaysia. pp. 98(1-4)."},{"key":"ref_17","unstructured":"Isa, M.D., Rahmat, M.F., and Husein, T.A. (, January June,). Image reconstruction algorithm for electrical charge tomography system. Malacca, Malaysia."},{"key":"ref_18","first-page":"252","article-title":"Process tomography system by electrical charge carried by particle","volume":"5","author":"Machida","year":"2005","journal-title":"IEEE Sen. J."},{"key":"ref_19","unstructured":"Yong, W.D., and Dong, F. (, January August). An image reconstruction algorithm based on regularization optimization for process tomography. Hong Kong, China."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/S0032-5910(00)00292-8","article-title":"Application of electrical tomography for gas-solid and liquid-solids flows\u2013a review","volume":"112","author":"Dyakowski","year":"2000","journal-title":"Power Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1088\/0957-0233\/12\/5\/304","article-title":"Image reconstruction in electrical capacitance tomography using multi linear regression and regularization","volume":"12","author":"Yan","year":"2001","journal-title":"Meas. Sci. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1007\/BF02219234","article-title":"Regularization GSVD and truncated GSVD","volume":"29","author":"Hansen","year":"1989","journal-title":"BIT"},{"key":"ref_23","first-page":"1","article-title":"An image reconstruction algorithm based on new objective function for electrical capacitance tomography","volume":"19","author":"Jing","year":"2008","journal-title":"Meas. Sci. Technol."},{"key":"ref_24","first-page":"193","article-title":"Numerical modeling and analysis of the forward and inverse problems in electrical capacitance tomography","volume":"1","author":"Soleimani","year":"2005","journal-title":"Int. J. Inf. Syst. Sci."},{"key":"ref_25","first-page":"103","article-title":"Regularization tools: A MATLAB package for analysis and solution of discrete ill-posed problem","volume":"4","author":"Hansen","year":"2007","journal-title":"Numer. Algorithm."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Su, M.X., Xu, F., Cai, X.S., Ren, K.F., and Shen, J.Q. Optimization of regularization parameter of inversion in particle sizing using light extinction method. Beijing, China. Volume 5.","DOI":"10.1016\/j.cpart.2007.04.005"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/9\/12\/10291\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:12:02Z","timestamp":1760220722000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/9\/12\/10291"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12,18]]},"references-count":26,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2009,12]]}},"alternative-id":["s91210291"],"URL":"https:\/\/doi.org\/10.3390\/s91210291","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12,18]]}}}