Modified tropical algebra based median filter for removing salt and pepper noise in digital image

Abstract

Noise is the information damage that may occur in the image due to the changes in information during the transmission process. In order to overcome these problems, it is necessary to do filtering process on the image. Until now many filtering algorithms have been proposed to remove noise. Most existing methods only work for low level noise. In this study, the authors proposed an efficient and easy‐to‐understand filtering algorithm using the concept of tropical algebra and singular value decomposition (SVD). The SVD will be used to detect noise in 3 × 3 templates. Furthermore, if noise is detected then new pixels will be obtained by using the concept of tropical operations. The results of this study show that the proposed method provides better results from the existing methods in terms of quantitative and visual.

Tropical algebra for noise removal and optimal control

“…Situation Two: A 1;1 < 0, A 2;2 < 0, A 3;3 ¼ 0: By equations ( 6), (10), and ( 14), we get A 1;2 þ A 2;1 < 0, A 3;2 þ A 2;3 < 0, A 1;3 þ A 3;1 < 0. By equation (7), we have A 1;2 ¼ A 1;3 þ A 3;2 . By equation (8), we obtain A 1;3 ¼ maxfA 1;2 þ A 2;3 , A 1;3 g, by equation ( 9) we know A 2;1 ¼ A 2;3 þ A 3;1 , by equation (11) we have A 2;3 ¼ maxfA 2;1 þ A 1;3 , A 2;3 g, by equation ( 12) we get A 3;1 ¼ maxfA 3;2 þ A 2;1 , A 3;1 g, and by equation ( 13) we obtain A 3;2 ¼ maxfA 3;1 þ A 1;2 , A 3;2 g.…”

“…In the same way, we can get A 2;3 > A 2;1 þ A 1;3 A 3;1 > A 3;2 þ A 2;1 , A 3;2 > A 3;1 þ A 1;2 . By equations (7) and (9) we have…”

“…6 The tropical addition is a good filtering algorithm to detect and remove the noise. 7 The tropical algebra has some special properties to describe discontinuous functions which are widely appeared in the optimal control. For example, we consider the following polynomial…”

Impulse Noise Removal Based on Hybrid Genetic Algorithm

“…Impulse noise removal is one of the essential issues in image processing, many approaches have been proposed to suppression of noise in digital images from the literature, and however, eliminate noise from digital images is still a difficult problem [1][2][3][4][5][6][7]. Different sensors, for example, laser scanners, medical scanners, cameras, and weather satellites, can obtain digital images, but these images might inherently be polluted by noise during acquisition compression processes, transmission [8][9][10][11]. It is essential to remove the noise while retaining the basic features of the image, such as edges and corners.…”

Adaptive switching interpolation filter for restoring impulse corrupted digital images

“…These learning dictionary contents in the form of sparse representation are later used by the learning algorithms for restoring corrupted images. Many recent approaches including adaptive probability filter [35], selective mean filter [36], effective hybrid genetic algorithm [37], adaptive frequency MF [38], improved based on pixel density filter [39], switching adaptive MF [40], total variation L1 fidelity salt‐and‐pepper denoising [41], based on pixel density filter [42], modified switching MF [43], modified tropical algebra‐based MF [44], recursive mean filter [45], radial basis function filter [46], and continued fractions interpolation filter [47] are also in the literature for restoring images contaminated with salt and pepper noise. All these algorithms limit their filtering process to restore only the impulsive positions of the image and find a suitable signal estimate from the nearest possible uncorrupted neighbourhood by adapting their filtering parameters.…”