{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T22:45:19Z","timestamp":1788389119070,"version":"build-2803163510"},"reference-count":23,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T00:00:00Z","timestamp":1769212800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"},{"start":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T00:00:00Z","timestamp":1769212800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100007631","name":"Chungnam National University Hospital","doi-asserted-by":"publisher","award":["2023\u2010CF\u2010007"],"award-info":[{"award-number":["2023\u2010CF\u2010007"]}],"id":[{"id":"10.13039\/501100007631","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2026,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Beam hardening is an unavoidable phenomenon in polychromatic CT systems, where lower\u2010energy photons are preferentially absorbed as x\u2010rays pass through materials such as tissue, bone, and metal. This energy\u2010dependent attenuation, which conflicts with the monochromatic assumption in filtered back\u2010projection (FBP), produces artifacts that degrade CT image quality and diagnostic accuracy.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>This study aims to quantitatively estimate the mean energy corresponding to the beam\u2010hardened projection data along each x\u2010ray path and to employ this mean energy to convert energy\u2010dependent projections into beam\u2010hardening\u2013corrected data. The effectiveness of the proposed mean energy\u2013based correction method is verified through numerical\u00a0simulations.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>To mathematically determine the mean energy, a polynomial equation\u00a0is derived whose solution represents the mean energy. Based on the Beer\u2013Lambert law, the CT system is formulated as an energy\u2010integrated model incorporating the x\u2010ray spectrum and the linear attenuation coefficient of the scanned object. By applying the mean value theorem for integrals and performing power series expansions of the energy\u2010dependent components of the attenuation coefficient\u2014such as Compton scattering and photoelectric absorption\u2014a polynomial equation\u00a0with respect to the mean energy is obtained. Solving this equation\u00a0yields the mean energy, which is subsequently employed to generate beam\u2010hardening\u2014corrected projection\u00a0data.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>A novel correction method based on the computed mean energy is proposed to transform energy\u2010dependent projection data into corresponding monochromatic data. Numerical simulations conducted on various models demonstrate that the proposed approach effectively corrects beam\u2010hardened projection data and substantially reduces beam\u2010hardening artifacts in reconstructed CT images. The method maintains accuracy even in complex scenarios involving multiple overlapping materials and metallic objects, without a significant increase in computational cost. Furthermore, the robustness of the proposed correction technique is confirmed under varying x\u2010ray spectra, verifying its potential applicability to practical CT\u00a0imaging.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>Grounded in physical modeling and analytical approximation, this study presents a mathematical formulation for estimating the mean energy corresponding to beam\u2010hardened projection data and develops a correction method that effectively mitigates beam\u2010hardening artifacts. The results highlight the potential of the proposed mean energy\u2014based correction as a practical and computationally efficient solution for improving CT image quality. However, as this study primarily focused on the computation of mean energy as an indicator of beam\u2010hardening severity, further research is required to apply and validate the proposed method using experimental and clinical data for comprehensive verification of its practical\u00a0applicability.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.70292","type":"journal-article","created":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T14:55:06Z","timestamp":1769266506000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["New beam hardened data correction and its application to artifact reduction in CT images"],"prefix":"10.1002","volume":"53","author":[{"given":"Sungwhan","family":"Kim","sequence":"first","affiliation":[{"name":"Hanbat National University Daejeon Republic Of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Soo\u2010Ho","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Dentistry Chungnam National University Hospital Daejeon Republic Of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mi\u2010Kyoung","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Dentistry Chungnam National University Hospital Daejeon Republic Of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jaemin","family":"Shin","sequence":"additional","affiliation":[{"name":"Hanbat National University Daejeon Republic Of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jong Hyun","family":"Seo","sequence":"additional","affiliation":[{"name":"Hanbat National University Daejeon Republic Of 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