# Convolved Feature Vector Based Adaptive Fuzzy Filter for Image De-Noising
###### Abstract  
In this paper, a convolved feature vector based adaptive fuzzy filter is proposed for impulse noise removal. The proposed filter follows traditional approach, i.e., detection of noisy pixels based on certain criteria followed by filtering process. In the first step, proposed noise detection mechanism initially selects a small layer of input image pixels, convolves it with a set of weighted kernels to form a convolved feature vector layer. This layer of features is then passed to fuzzy inference system, where fuzzy membership degrees and reduced set of fuzzy rules play an important part to classify the pixel as noise-free, edge or noisy. Noise-free pixels in the filtering phase remain unaffected causing maximum detail preservation whereas noisy pixels are restored using fuzzy filter. This process is carried out traditionally starting from top left corner of the noisy image to the bottom right corner with a stride rate of one for small input layer and a stride rate of two during convolution. Convolved feature vector is very helpful in finding the edge information and hidden patterns in the input image that are affected by noise. The performance of the proposed study is tested on large data set using standard performance measures and the proposed technique outperforms many existing state of the art techniques with excellent detail preservation and effective noise removal capabilities. image de-noising; fuzzy logic; divide and conquer strategy; fuzzy reasoning; adaptive threshold 2023  
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[PERSON], [PERSON]  
A number of linear and non-linear image de-noising techniques have been proposed during the last few decades. Linear techniques replace noisy pixels by average value of the kernel causing blurry effects on the edges due to the removal of crisp information. On the other hand, non-linear techniques [3; 4; 5; 6; 7; 8; 9; 10] are preferred over linear techniques [11; 12; 13] because of their non-linear nature and robustness against noise. These techniques do not interrupt the image details to great extent causing better restored results. In this review section, we will focus mainly on non-linear techniques. The main filter in non-linear techniques is median filter, easy in implementation, and is used as most common tool in many other techniques. It gives best performance for images having smooth variations and low level of impulse noise but gives inadequate performance for highly contrast detailed images corrupted with high noise densities because its mechanism simply use median to replace the central corrupted pixel in both the cases. Furthermore, edges [14] are most important parts of the image and they are directly affected by the size of the kernel. So design of the kernel in non-linear filters is equally important to avoid blurring effects at edges. Kernel with a small size (say \(3\times 3\)) is very effective for low noise densities or where the total number of corrupted pixels are fewer than half of the size of kernel. Kernel sizes greater than previously described size might smear lines and edges in detailed regions of the image due to indiscriminate gray level substitutions. In last few decades, a large number of variations [4; 5; 6; 7; 8; 9; 10; 15; 16; 17; 18] have been proposed in median filter to enhance its computational power, detail preservation and noise suppression capabilities. Median filters based techniques [4; 5; 6; 7; 8; 9; 10] simply replace the degraded pixel value by median of neighborhood pixels whereas weighted median techniques [5; 6; 8; 16] use weighing mechanism for good and bad ones. All of the above filters are efficient against impulse noise but fail due to blurring [11; 12; 13] at edges and loss of actual details in an image. Switching mechanisms [9; 17], fuzzy based techniques [19; 20; 21; 22; 23; 24; 25; 26; 27; 28], directional filters [15; 16; 22; 24] and others [29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39] are good de-noising filters against random and universal noise but still lacking in detail preservation due to poor or no proper edge detection.