Adaptive image restoration by a novel neuro-fuzzy approach using complex fuzzy sets

A complex neuro-fuzzy approach using new concept of complex fuzzy sets and neuro-fuzzy system is presented to deal with the problem of adaptive image noise cancelling (AINC). An image can be tainted by unknown noise, resulting in the degradation of valuable image information. A complex fuzzy set (CFS) is characterised in the unit disc of the complex plane by a complex-valued membership function that includes an amplitude function and a phase function. Based on the nature of CFSs, several CFSs can be used to design a complex neural fuzzy system (CNFS) for the application of AINC. To train the CNFS, a hybrid learning method is used, where the algorithm of artificial bee colony (ABC) and the method of recursive least squares estimator (RLSE) are integrated in a complementarily hybrid way. Three cases are used to test the proposed CNFS for image restoration. The experimental results by the proposed CNFS approach are compared with those by other approaches and the proposed approach has shown promising performance.