Łukasiewicz transform and its application to compression and reconstruction of digital images

Information Sciences

Volumn 177, Issue 6, 2007, Pages 1481-1498

  Di Nola, A ^a   Russo, C ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

Fuzzy relation equations; Many valued logic; MV algebras; Residuated maps

Indexed keywords

ALGORITHMS; CONFORMAL MAPPING; IMAGE COMPRESSION; IMAGE PROCESSING; IMAGE RECONSTRUCTION; LINEAR ALGEBRA;

FUZZY RELATION EQUATIONS; MANY VALUED LOGIC; MV-ALGEBRAS; RESIDUATED MAPS;

MATHEMATICAL TRANSFORMATIONS;

EID: 33845932089     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2006.09.002     Document Type: Article

References (20)

1. Cignoli R.L.O., D'Ottaviano I.M.L., and Mundici D. Algebraic Foundations of Many-valued Reasoning, Trends in Studia Logica (2000), Kluwer Academic Publishers, Dordrecht
2. Cohen G., Gaubert S., and Quadrat J.-P. Hahn-Banach separation theorem for max-plus semimodules. In: Menaldi J.-L., Rofman E., and Sulem A. (Eds). Optimal Control and Partial Differential Equations. Proceedings of Conference in honour of Professor Alain Bensoussan's 60th birthday, December 4-5, 2000, Paris (2000), IOS Press, Amsterdam 325-334
3. Di Nola A., and Gerla B. Algebras of Łukasiewicz's logic and their semiring reducts. Idempotent Mathematics and Mathematical Physics. Contemp. Math. vol. 377 (2005), American Mathematical Society, Providence, RI 131-144
4. Di Nola A., and Lettieri A. On normal forms in Łukasiewicz logic. Arch. Math. Logic 43 6 (2004) 795-823
5. Di Nola A., Sessa S., Pedrycz W., and Sanchez E. Fuzzy Relation Equations and their Applications to Knowledge Engineering (1989), Kluwer Academic Publishers, Dordrecht
6. Feig E., and Winograd S. Fast algorithms for the discrete cosine transform. IEEE Trans. Signal Processing 40 September (1992) 2174-2193
7. Golan J.S. The Theory of Semirings with Applications in Mathematics and Theoretical Computer Science (1992), Longman Scientific and Technical, Harlow and Wiley, New York
8. Hirota K., Kawamoto K., Nobuhara H., and Yoshida S.I. On a lossy image compression/reconstruction method based on fuzzy relational equations. Iran. J. Fuzzy Syst. 1 (2004) 33-42
9. Hirota K., Nobuhara H., and Pedrycz W. Relational image compression: optimizations through the design of fuzzy coders and YUV color space. Soft Computing 9 (2005) 471-479
10. Hirota K., and Pedrycz W. Fuzzy relational compression. IEEE Trans. Syst. Man Cybernet. B 29 3 (1999) 407-415
11. Hung A.C., and Meng T.H.-Y. A comparison of fast DCT algorithms. Multimedia Systems 2 5 (1994)
12. Kwak K.-C., and Pedrycz W. Face recognition using fuzzy integral and wavelet decomposition method. IEEE Trans. Syst. Man Cybernet. B 34 4 (2004) 1666-1675
13. Loia V., and Sessa S. Fuzzy relation equations for coding/decoding processes of images and videos. Inform. Sci. 171 1-3 (2005) 145-172
14. M. Nachtegael, D. Van der Weken, D. Van De Ville, E.E. Kerre, W. Philips, I. Lemahieu, An overview of fuzzy and fuzzy-classical filters for noise reduction, in: Proceedings of the 10th FUZZ-IEEE Conference, 2001, pp. 3-6.
15. H. Nobuhara, W. Pedrycz, K. Hirota, A digital watermarking algorithm using image compression method based on fuzzy relational equations, in: IEEE Int. Conference Fuzzy Syst., Proc Hawaii, 2002 (CD-ROM).
16. Nobuhara H., Pedrycz W., and Hirota K. Fast solving method of fuzzy relational equations and its application to image compression/reconstruction. IEEE Trans. Fuzzy Syst. 8 3 (2000) 325-334
17. Nobuhara H., Takama Y., and Hirota K. Image compression/reconstruction based on various types of fuzzy relational equations. Trans. Inst. Electrical Eng. Japan 121-C 6 (2001) 1102-1113
18. Perfilieva I. Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157 (2006) 993-1023
19. Available from: .
20. Available from: .