In healthcare systems, minimizing storage needs, transmission bandwidth, and processing expenses requires effective medical picture compression. This paper provides a thorough analysis of the many methods and strategies used in medical image compression. The difficulties of precisely compressing medical picture data are examined, particularly the requirement to preserve diagnostic quality at high compression ratios. More modern strategies like deep learning-based compression techniques are contrasted with more established ones like JPEG and JPEG2000 compression. The usage of neural networks, autoencoders, and generative adversarial networks (GANs) as well as other lossless and lossy compression techniques are also explored in this research. The suggested method makes use of CNN-RNN-AE to learn a condensed version of the original image, which had structural information. Multilayer perceptron's (MLPs) were utilized for lossless image compression, while autoencoders and generative adversarial networks (GANs) were employed for lossy compression. The original image was then recovered by decoding the encoded image using a high-quality reconstruction approach. The optimal compression technique that has been provided fits in with the current image codec standards. A variety of experiment outcomes were compared with JPEG, JPEG2000, binary tree, and optimal truncation in terms of space saving (SS), reconstructed image quality, and compression efficiency. The results support the effectiveness of the designed strategy.