Image denoising using generalised Cauchy filter

Abstract

In many image processing analysis, it is important to significantly reduce the noise level. This study aims at introducing an efficient method for this purpose based on generalised Cauchy (GC) distribution. Therefore, some characteristics of GC distribution is considered. In particular, the characteristic function of a GC distribution is derived by using the theory of positive definite densities and utilising the density of a GC random variable as the characteristic function of a convolution of two generalised non-symmetric Linnik variables. Further, GC distribution is considered as a filter and in the proposed method for image noise reduction the optimal parameters of GC filter is defined by using the particle swarm optimisation. The proposed method is applied to different types of noisy images and the obtained results are compared with four state-of-the-art denoising algorithms. Experimental results confirm that their method could significantly reduce the noise effect.