At present, there is an increase in the capacity of data generated and stored in the medical area. Thus, for the efficient handling of these extensive data, the compression methods need to be re-explored by considering the algorithm’s complexity. To reduce the redundancy of the contents of the image, thus increasing the ability to store or transfer information in optimal form, an image processing approach needs to be considered. So, in this study, two compression techniques, namely lossless compression and lossy compression, were applied for image compression, which preserves the image quality. Moreover, some enhancing techniques to increase the quality of a compressed image were employed. These methods were investigated, and several comparison results are demonstrated. Finally, the performance metrics were extracted and analyzed based on state-of-the-art methods. PSNR, MSE, and SSIM are three performance metrics that were used for the sample medical images. Detailed analysis of the measurement metrics demonstrates better efficiency than the other image processing techniques. This study helps to better understand these strategies and assists researchers in selecting a more appropriate technique for a given use case.