Digital image is considered as a powerful tool to carry and transmit information between people. Thus, it attracts the attention of large number of researchers, among them those interested in preserving the image features from any factors that may reduce the image quality. One of these factors is the noise which affects the visual aspect of the image and makes others image processing more difficult. Thus far, solving this noise problem remains a challenge for the researchers in this field. A lot of image denoising techniques have been introduced in order to remove the noise by taking care of the image features; in other words, getting the best similarity to the original image from the noisy one. However, the findings are still inconclusive. Beside the enormous amount of researches and studies which adopt several mathematical concepts (statistics, probabilities, modeling, PDEs, wavelet, fuzzy logic, etc.), there is also the scarcity of review papers which carry an important role in the development and progress of research. Thus, this review paper intorduce an overview of the different fundamental approaches that yield the several image-denoising techniques, presented with a new classification. Furthermore, the paper presents the different evaluation tools needed on the comparison between these techniques in order to facilitate the processing of this noise problem, among a great diversity of techniques and concepts.

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.

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An image through the digitization process is referred to as a digital image. The quality of the digital image may be degenerating due to interferences on the acquisition, transmission, extraction, etc. This attracted the attention of many researchers to study the causes of damage to the information in the image. In addition to finding cause of image damage, the researchers also looking for ways to overcome this problem. There are many filtering techniques that have been introduced to deal the damage to the information in the image. In addition to eliminating noise from the image, filtering techniques also aims to maintain the originality of the features in the image. Among the many research papers on image filtering there is a lack of review papers which are an important to facilitate researchers in understanding the differences in each filtering technique. Additionally, it helps researchers determine the direction of research conducted based on the results of previous research. Therefore, this paper presents a review of several filtering techniques that have been developed so far.

Removing noise from the image by retaining the details and features of this treated image remains a standing challenge for the researchers in this field. Therefore, this study is carried out to propose and implement a new denoising technique for removing impulse noise from the digital image, using a new way. This technique permits the narrowing of the gap between the original and the restored images, visually and quantitatively by adopting the mathematical concept ''arithmetic progression''. Through this paper, this concept is integrated into the image denoising, due to its ability in modelling the variation of pixels' intensity in the image. The principle of the proposed denoising technique relies on the precision, where it keeps the uncorrupted pixels by using effective noise detection and converts the corrupted pixels by replacing them with other closest pixels from the original image at lower cost and with more simplicity.