Removing noise in a digital image using a new entropy method based on intuitionistic fuzzy sets

We propose a novel framework which is aimed to process gray images. By appropriately converting digital colors to intuitionistic fuzzy numbers in a generalized framework, the algorithm tends to remove noise impairments while processing the damaged images. A new entropy measure on intuitionistic fuzzy sets is introduced for determining the uncertainty of each pixel and consequently, to recognize the best processed image which has the least noise. We conclude by discussing two illustrative examples for verifying the developed approach.

[1]  Janusz Kacprzyk,et al.  Entropy for intuitionistic fuzzy sets , 2001, Fuzzy Sets Syst..

[2]  Qiang Zhang,et al.  Multicriteria decision making method based on intuitionistic fuzzy weighted entropy , 2011, Expert Syst. Appl..

[3]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[4]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[5]  Tamaz Gachechiladze,et al.  Entropy of fuzzy events , 1997, Fuzzy Sets Syst..

[6]  Beloslav Riečan,et al.  The entropy of fuzzy dynamical systems , 1997 .

[7]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[8]  Pabitra Kumar Maji,et al.  More on Intuitionistic Fuzzy Soft Sets , 2009, RSFDGrC.

[9]  M. T. Lamata,et al.  Entropy measures associated with a fuzzy basic probability assignment , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[10]  Fakhri Karray,et al.  Fuzzy entropy: a brief survey , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[11]  Humberto Bustince,et al.  Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets , 1996, Fuzzy Sets Syst..

[12]  André Bigand,et al.  Fuzzy filter based on interval-valued fuzzy sets for image filtering , 2010, Fuzzy Sets Syst..

[13]  L. Zadeh Probability measures of Fuzzy events , 1968 .

[14]  Dagmar Markechová,et al.  The entropy of fuzzy dynamical systems, general scheme and generators , 1998, Fuzzy Sets Syst..

[15]  Luís Corte-Real,et al.  Removal of blotches and line scratches from film and video sequences using a digital restoration chain , 1999, NSIP.

[16]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[17]  Okyay Kaynak,et al.  Entropy-based operations on fuzzy sets , 1998, IEEE Trans. Fuzzy Syst..

[18]  Ioannis K. Vlachos,et al.  Intuitionistic fuzzy information - Applications to pattern recognition , 2007, Pattern Recognit. Lett..

[19]  Humberto Bustince,et al.  Image segmentation using Atanassov's intuitionistic fuzzy sets , 2013, Expert systems with applications.

[20]  Alireza Rezvanian,et al.  An efficient method for impulse noise reduction from images using fuzzy cellular automata , 2012 .

[21]  Brijendra Kumar Joshi,et al.  A Review Paper: Noise Models in Digital Image Processing , 2015, ArXiv.

[22]  Jaroslav Vlach,et al.  Fuzzy Methods and Image Fusion in a Digital Image Processing , 2012 .