{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:27:42Z","timestamp":1777645662037,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["FI"],"published-print":{"date-parts":[[2023,8,1]]},"abstract":"<jats:p>Discrete tomography focuses on the reconstruction of functions from their line sums in a finite number d of directions. In this paper we consider functions f : A \u2192 R where A is a finite subset of \u21242 and R an integral domain. Several reconstruction methods have been introduced in the literature. Recently Ceko, Pagani and Tijdeman developed a fast method to reconstruct a function with the same line sums as f. Up to here we assumed that the line sums are exact. Some authors have developed methods to recover the function f under suitable conditions by using the redundancy of data. In this paper we investigate the case where a small number of line sums are incorrect as may happen when discrete tomography is applied for data storage or transmission. We show how less than d\/2 errors can be corrected and that this bound is the best possible. Moreover, we prove that if it is known that the line sums in k given directions are correct, then the line sums in every other direction can be corrected provided that the number of wrong line sums in that direction is less than k\/2.<\/jats:p>","DOI":"10.3233\/fi-222154","type":"journal-article","created":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T10:46:11Z","timestamp":1690886771000},"page":"91-112","source":"Crossref","is-referenced-by-count":0,"title":["Error Correction for Discrete Tomography"],"prefix":"10.1177","volume":"189","author":[{"given":"Matthew","family":"Ceko","sequence":"first","affiliation":[{"name":"School of Physics and Astronomy Monash University, Melbourne, Australia, matthew.ceko@gmail.com"}]},{"given":"Lajos","family":"Hajdu","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University of Debrecen, Debrecen, Hungary, hajdul@science.unideb.hu"}]},{"given":"Rob","family":"Tijdeman","sequence":"additional","affiliation":[{"name":"Mathematical Institute, Leiden University, Leiden, The Netherlands, tijdeman@ziggo.nl"}]}],"member":"179","container-title":["Fundamenta Informaticae"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/FI-222154","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:32:51Z","timestamp":1777444371000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/FI-222154"}},"subtitle":[],"editor":[{"given":"Paolo","family":"Dulio","sequence":"additional","affiliation":[]},{"given":"Andrea","family":"Frosini","sequence":"additional","affiliation":[]},{"given":"Grzegorz","family":"Rozenberg","sequence":"additional","affiliation":[]},{"given":"Lama","family":"Tarsissi","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2023,8,1]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.3233\/fi-222154","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,1]]}}}