Self-learning complex neuro-fuzzy system with complex fuzzy sets and its application to adaptive image noise canceling

In this paper we propose a new self-learning complex neuro-fuzzy system (CNFS) using complex fuzzy sets (CFSs). We design a class of Gaussian complex fuzzy sets for the proposed approach. This new computing model is applied to the problem of adaptive image noise canceling (AINC), where images are corrupted additively by unknown noise and the proposed CNFS is used to adaptively perform the task of image restoration. The proposed CNFS is focused on improving image quality with additive noise. The knowledge base of CNFS is composed of Takagi–Sugeno fuzzy If–Then rules, whose premises are described by CFSs. CFS is an advanced fuzzy set, which is described by a complex-valued membership function in the unit disc of the complex plane. The utility of CFSs can enhance the non-linear functional mapping ability of the CNFS, because CFSs can carry more information into fuzzy inference computing as well as more degrees of freedom for the adaption flexibility of CNFS. For optimal estimation of the parameters of CNFS, we devise a hybrid PSO–RLSE optimization method, which combines the well-known particle swarm optimization (PSO) method and the famous recursive least squares estimation (RLSE) method. Iteratively, the PSO is used to evolve the premise parameters of CNFS, based on which the RLSE is used to update the consequent parameters. The PSO–RLSE method is very efficient for fast learning. For AINC application, the proposed CNFS is used to mimic the behavior of unknown noise channel, so that corrupted images may be adaptively restored as close to its original version as possible. Several images are used to test the proposed approach, whose experimental results are compared to other approaches. The experimental results indicate that the proposed approach outperforms the compared approaches. Excellent performance for image restoration by the proposed approach has been observed.