# Hybrid Filter Based on Fuzzy Techniques for Mixed Noise Reduction in Color Images
## 1 Introduction  
Noise suppression is of great interest in digital image processing, considering that the quality improvement of corrupted images is of essential importance for the majority of image processing areas, including analysis of images, detection of edges, and pattern recognition. Digital images may be deteriorated by diverse types of noise, generated by different causes, such as signal instabilities, defective sensors, physical deterioration of the material due to aging, poor lighting conditions, errors in the transmission due to channel noise, or interference caused by electromagnetic fields. Consequently, digital images are deteriorated by noise. Impulsive noise, Gaussian noise, and a mixture of them are among the most usual kinds of noise [1]. The elimination of mixed, Gaussian-impulsive noise is a tough task, as methods built to suppress impulses are inefficacious in the Gaussian noise elimination and the methods introduced to reduce Gaussian noise are not capable of removing impulses [1, 2]. The widely known vector median filter (VMF) [3] and its variants [4, 5] efficaciously reduce the impulses in color images; however, as the output of this filter corresponds to one of the pixels of the neighborhood, this method is not efficient reducing the Gaussian disturbance. To relieve this difficulty, the reduced ordering approach is employed to suppress the noise in color images [6, 7, 8]. Another approach for reducing mixed Gaussian-impulsive noise is based on the switching methods [9, 10, 11]. This technique has been used in color [10] and in grayscale images [9, 11]. These methods aim to detect the impulsive pixels and reduce them, employing a convenient technique, and process the rest of pixels with a method created to reduce Gaussian noise. The peer group concept proposedin [12; 13] and its fuzzy variants [10; 14] has also been employed to reduce mixed noise in color digital images. These filters perform an impulse detection stage followed by an averaging replacement stage. Another family of methods for color image denoising is founded on the idea of geodesic digital paths [15; 16; 17]. In [18] an efficient trilateral filter (TF) to eliminate the mixed noise in grayscale images, was introduced. In this filter, an impulsive noise detector founded on the rank ordered absolute differences statistic (ROAD) is combined with the bilateral filter [19]. In [20], a method for the filtering of images contaminated with uniform impulse and Gaussian noise was proposed. The method combines the kernel regression framework and a Bayesian classification. This method was proposed for grayscale and color images. The partition-based methods for noise suppression in color digital images [21; 22] arrange the pixels in different signal activity classes, which are associated to adequate denoising methods. Another important class of filters are the regularization methods [23; 24; 25; 26] founded on partial differential equations. These methods have been employed for color [23; 24] and grayscale images [25]. Another important family of denoising methods was founded on the improved intersection of confidence intervals [27; 28; 29]. In [27] a fast denoising algorithm for video signals is proposed, and in [28] an adaptive denoising method for X-ray images is presented. In [29] the local entropy concept is introduced for denoising and removing tissue in X-ray images. The fuzzy technique has also been employed to eliminate mixed noise in color digital images; e.g., [30; 31; 32; 10]. A fuzzy method based on weighted averaging is proposed in [30] to suppress mixed impulsive-Gaussian disturbances in color digital images. In this method, a weighted averaging is performed on the pixels inside the filtering window. The authors used a fuzzy rule system in order to adaptively calculate the weights. [PERSON] et al. [31] presented a two stage fuzzy method for the elimination of mixed impulse-Gaussian distortions in color digital images.