Conclusions and some possible directions for future study are presented in Section “ Conclusions”. Section “ Experiments” presents extensive experiments and discussion. Sections “ Classical denoising method, Transform techniques in image denoising, CNN-based denoising methods” summarize the denoising techniques proposed up to now. In Section “ Image denoising problem statement”, we give the formulation of the image denoising problem. The remainder of this paper is organized as follows. In recent decades, great achievements have been made in the area of image denoising, and they are reviewed in the following sections. The main reason for this is that from a mathematical perspective, image denoising is an inverse problem and its solution is not unique. However, it remains a challenging and open task. In fact, image denoising is a classic problem and has been studied for a long time. Overall, recovering meaningful information from noisy images in the process of noise removal to obtain high quality images is an important problem nowadays. However, since noise, edge, and texture are high frequency components, it is difficult to distinguish them in the process of denoising and the denoised images could inevitably lose some details. Image denoising is to remove noise from a noisy image, so as to restore the true image. Therefore, image denoising plays an important role in modern image processing systems. With the presence of noise, possible subsequent image processing tasks, such as video processing, image analysis, and tracking, are adversely affected. Owing to the influence of environment, transmission channel, and other factors, images are inevitably contaminated by noise during acquisition, compression, and transmission, leading to distortion and loss of image information.
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