Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method
Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing...
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| Veröffentlicht in: | ISA transactions 2012-11, Vol.51 (6), p.808-820 |
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| creator | Wang, Qi Wang, Huaxiang Cui, Ziqiang Yang, Chengyi |
| description | Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing.
► The expectation maximization method is used to solve the inverse problem for EIT. ► The mathematical model of EIT is transformed to likelihood minimization problem. ► The noise level of the measurement system is considered as prior information. ► The EM method can obtain a non-negative solution and low image distortion. ► The EM method is robust to measurement noise. |
| doi_str_mv | 10.1016/j.isatra.2012.04.011 |
| format | Article |
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► The expectation maximization method is used to solve the inverse problem for EIT. ► The mathematical model of EIT is transformed to likelihood minimization problem. ► The noise level of the measurement system is considered as prior information. ► The EM method can obtain a non-negative solution and low image distortion. ► The EM method is robust to measurement noise.</description><identifier>ISSN: 0019-0578</identifier><identifier>EISSN: 1879-2022</identifier><identifier>DOI: 10.1016/j.isatra.2012.04.011</identifier><identifier>PMID: 22664353</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Algorithms ; Applied sciences ; Artificial intelligence ; Computer science; control theory; systems ; Computer Simulation ; Control theory. Systems ; Cross-disciplinary physics: materials science; rheology ; Diagnosis, Computer-Assisted - methods ; Electrical impedance ; Electrical impedance tomography (EIT) ; Exact sciences and technology ; Expectation maximization (EM) method ; Humans ; Image reconstruction ; Inverse problems ; Likelihood Functions ; Materials science ; Materials testing ; Mathematical analysis ; Mathematical models ; Maximization ; Modelling and identification ; Models, Biological ; Models, Statistical ; Pattern recognition. Digital image processing. Computational geometry ; Physics ; Plethysmography, Impedance - methods ; Statistical method ; Statistical methods ; Tomography</subject><ispartof>ISA transactions, 2012-11, Vol.51 (6), p.808-820</ispartof><rights>2012 ISA</rights><rights>2015 INIST-CNRS</rights><rights>Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c425t-f862da2e84a9372210a6d5272547efbabf4148fbb9143cf75e23fb1383018bea3</citedby><cites>FETCH-LOGICAL-c425t-f862da2e84a9372210a6d5272547efbabf4148fbb9143cf75e23fb1383018bea3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.isatra.2012.04.011$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>315,781,785,3551,27929,27930,46000</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26376172$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/22664353$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Wang, Qi</creatorcontrib><creatorcontrib>Wang, Huaxiang</creatorcontrib><creatorcontrib>Cui, Ziqiang</creatorcontrib><creatorcontrib>Yang, Chengyi</creatorcontrib><title>Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method</title><title>ISA transactions</title><addtitle>ISA Trans</addtitle><description>Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing.
► The expectation maximization method is used to solve the inverse problem for EIT. ► The mathematical model of EIT is transformed to likelihood minimization problem. ► The noise level of the measurement system is considered as prior information. ► The EM method can obtain a non-negative solution and low image distortion. ► The EM method is robust to measurement noise.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Computer science; control theory; systems</subject><subject>Computer Simulation</subject><subject>Control theory. Systems</subject><subject>Cross-disciplinary physics: materials science; rheology</subject><subject>Diagnosis, Computer-Assisted - methods</subject><subject>Electrical impedance</subject><subject>Electrical impedance tomography (EIT)</subject><subject>Exact sciences and technology</subject><subject>Expectation maximization (EM) method</subject><subject>Humans</subject><subject>Image reconstruction</subject><subject>Inverse problems</subject><subject>Likelihood Functions</subject><subject>Materials science</subject><subject>Materials testing</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Maximization</subject><subject>Modelling and identification</subject><subject>Models, Biological</subject><subject>Models, Statistical</subject><subject>Pattern recognition. Digital image processing. Computational geometry</subject><subject>Physics</subject><subject>Plethysmography, Impedance - methods</subject><subject>Statistical method</subject><subject>Statistical methods</subject><subject>Tomography</subject><issn>0019-0578</issn><issn>1879-2022</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqFkc1u1DAURi0EotPCGyDkDVK7SOq_xM4GCVVtqVRUCZW15TjXHQ_JONgOat--HmaAHay8uOe7vvoOQu8oqSmh7fmm9snkaGpGKKuJqAmlL9CKKtlVjDD2Eq0IoV1FGqmO0HFKG0IIazr1Gh0x1raCN3yFvn8FG7Ypx8VmH7Y4OAwj2By9NSP20wyD2VrAOUzhIZp5_YRPL2_uz8rIPEDCvUkw4BLMa8DwOJeo-bVoMo9-WqZCfznDE-R1GN6gV86MCd4e3hP07ery_uJzdXt3fXPx6baygjW5cqplg2GghOm4ZIwS0w4Nk6wRElxveieoUK7vOyq4dbIBxl1PueKEqh4MP0Gn-71zDD8WSFlPPlkYR7OFsCRNKW-blivC_o8SQUtrqpMFFXvUxpBSBKfnWEqITwXSOyN6o_dG9M6IJkIXIyX2_vDD0k8w_An9VlCADwfApNK5i6Vvn_5yLZctlbtTP-45KNX99BB1sh6Km8HH0roegv_3Jc-S6arJ</recordid><startdate>20121101</startdate><enddate>20121101</enddate><creator>Wang, Qi</creator><creator>Wang, Huaxiang</creator><creator>Cui, Ziqiang</creator><creator>Yang, Chengyi</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>7SC</scope><scope>7SP</scope><scope>7TA</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JG9</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20121101</creationdate><title>Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method</title><author>Wang, Qi ; Wang, Huaxiang ; Cui, Ziqiang ; Yang, Chengyi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c425t-f862da2e84a9372210a6d5272547efbabf4148fbb9143cf75e23fb1383018bea3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Computer science; control theory; systems</topic><topic>Computer Simulation</topic><topic>Control theory. Systems</topic><topic>Cross-disciplinary physics: materials science; rheology</topic><topic>Diagnosis, Computer-Assisted - methods</topic><topic>Electrical impedance</topic><topic>Electrical impedance tomography (EIT)</topic><topic>Exact sciences and technology</topic><topic>Expectation maximization (EM) method</topic><topic>Humans</topic><topic>Image reconstruction</topic><topic>Inverse problems</topic><topic>Likelihood Functions</topic><topic>Materials science</topic><topic>Materials testing</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Maximization</topic><topic>Modelling and identification</topic><topic>Models, Biological</topic><topic>Models, Statistical</topic><topic>Pattern recognition. Digital image processing. Computational geometry</topic><topic>Physics</topic><topic>Plethysmography, Impedance - methods</topic><topic>Statistical method</topic><topic>Statistical methods</topic><topic>Tomography</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Qi</creatorcontrib><creatorcontrib>Wang, Huaxiang</creatorcontrib><creatorcontrib>Cui, Ziqiang</creatorcontrib><creatorcontrib>Yang, Chengyi</creatorcontrib><collection>Pascal-Francis</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>ISA transactions</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Qi</au><au>Wang, Huaxiang</au><au>Cui, Ziqiang</au><au>Yang, Chengyi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method</atitle><jtitle>ISA transactions</jtitle><addtitle>ISA Trans</addtitle><date>2012-11-01</date><risdate>2012</risdate><volume>51</volume><issue>6</issue><spage>808</spage><epage>820</epage><pages>808-820</pages><issn>0019-0578</issn><eissn>1879-2022</eissn><abstract>Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing.
► The expectation maximization method is used to solve the inverse problem for EIT. ► The mathematical model of EIT is transformed to likelihood minimization problem. ► The noise level of the measurement system is considered as prior information. ► The EM method can obtain a non-negative solution and low image distortion. ► The EM method is robust to measurement noise.</abstract><cop>Kidlington</cop><pub>Elsevier Ltd</pub><pmid>22664353</pmid><doi>10.1016/j.isatra.2012.04.011</doi><tpages>13</tpages></addata></record> |
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| subjects | Algorithms Applied sciences Artificial intelligence Computer science control theory systems Computer Simulation Control theory. Systems Cross-disciplinary physics: materials science rheology Diagnosis, Computer-Assisted - methods Electrical impedance Electrical impedance tomography (EIT) Exact sciences and technology Expectation maximization (EM) method Humans Image reconstruction Inverse problems Likelihood Functions Materials science Materials testing Mathematical analysis Mathematical models Maximization Modelling and identification Models, Biological Models, Statistical Pattern recognition. Digital image processing. Computational geometry Physics Plethysmography, Impedance - methods Statistical method Statistical methods Tomography |
| title | Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method |
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