{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:51:26Z","timestamp":1760241086276,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T00:00:00Z","timestamp":1575331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We present a fast algorithm that improves on the performance of the multilevel fuzzy transform image compression method. The multilevel F-transform (for short, MF-tr) algorithm is an image compression method based on fuzzy transforms that, compared to the classic fuzzy transform (F-transform) image compression method, has the advantage of being able to reconstruct an image with the required quality. However, this method can be computationally expensive in terms of execution time since, based on the compression ratio used, different iterations may be necessary in order to reconstruct the image with the required quality. To solve this problem, we propose a fast variation of the multilevel F-transform algorithm in which the optimal compression ratio is found in order to reconstruct the image in as few iterations as possible. Comparison tests show that our method reconstructs the image in at most half of the CPU time used by the MF-tr algorithm.<\/jats:p>","DOI":"10.3390\/axioms8040135","type":"journal-article","created":{"date-parts":[[2019,12,4]],"date-time":"2019-12-04T04:30:35Z","timestamp":1575433835000},"page":"135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A Fast Multilevel Fuzzy Transform Image Compression Method"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5690-5384","authenticated-orcid":false,"given":"Ferdinando","family":"Di Martino","sequence":"first","affiliation":[{"name":"Dipartimento di Architettura, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"},{"name":"Centro Interdipartimentale Alberto CalzaBini, Universit\u00e0 degli Studi di Napoli Federico II, 80134 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1531-1111","authenticated-orcid":false,"given":"Irina","family":"Perfilieva","sequence":"additional","affiliation":[{"name":"Institute for Research and Applications of Fuzzy Modeling, Dvo\u0159\u00e1kova 7, 701 03 Ostrava, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4303-2884","authenticated-orcid":false,"given":"Salvatore","family":"Sessa","sequence":"additional","affiliation":[{"name":"Dipartimento di Architettura, Universit\u00e0 degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy"},{"name":"Centro Interdipartimentale Alberto CalzaBini, Universit\u00e0 degli Studi di Napoli Federico II, 80134 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1016\/j.fss.2005.11.012","article-title":"Fuzzy transforms","volume":"157","author":"Perfilieva","year":"2006","journal-title":"Fuzzy Sets Syst."},{"key":"ref_2","first-page":"2349","article-title":"Compression and decompression of images with discrete fuzzy transforms","volume":"17","author":"Sessa","year":"2007","journal-title":"Inf. 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