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In medical imaging systems, denoising is one of the important image processing tasks. Automatic noise removal will improve the quality of diagnosis and requires careful treatment of obtained imagery. Com-puted tomography (CT) and X-Ray imaging systems use the X radiation to capture images and they are usually corrupted by noise following a Poisson distribution. Due to the importance of Poisson noise re-moval in medical imaging, there are many state-of-the-art methods that have been studied in the image processing literature. These include methods that are based on total variation (TV) regularization, wave-lets, principal component analysis, machine learning etc. In this work, we will provide a review of the following important Poisson removal methods: the method based on the modified TV model, the adaptive TV method, the adaptive non-local total variation method, the method based on the higher-order natural image prior model, the Poisson reducing bilateral filter, the PURE-LET method, and the variance stabi-lizing transform-based methods. Our task focuses on methodology overview, accuracy, execution time and their advantage/disadvantage assessments. The goal of this paper is to provide an apt choice of denoising method that suits to CT and X-ray images. The integration of several high-quality denoising methods in image processing software for medical imaging systems will be always excellent option and help further image analysis for computer-aided diagnosis.