Tropical algebra based adaptive filter for noise removal in digital image

The concept of the tropical algebra was first introduced to solve problems in mathematical economy such as optimization and approximation problems. In this paper, the concept of tropical algebra is used to build an image filtering algorithm. By using this concept, the lowest and highest pixel values are considered in determining the new pixel value. In addition, adaptive window will also be implemented to help the filtering process become more effective at high density noise. Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) are used to evaluate the output image quality produced by the filtering method. In this experiment, the performance of proposed method and existing methods such as switching median filter (SMF), adaptive fuzzy noise switching median filter (NAFSM), modified decision based on unsymmetric trimmed median filter (MDBUTMF), adaptive type-2 fuzzy filter (AT2FF) ), based on pixel density filters (BPDF), different applied median filters (DAMF), and tropical SVD filters (TSVD) will be compared. PSNR and SSIM results show that the proposed method outperforms most existing methods: SMF (27.13/0.7954), NAFSM (29.11/0.8459), MDBTUMF (29.18/0.8462), AT2FF (28.10/0.8159), BPDF (25.65/0.7545), DAMF (31.20/0.8833), TSVD (28.39/0.7906), and proposed (31.26/0.8827).