The storage as well as access of health-related imaging have been revolutionized by cloud-based systems. Algorithms for effective compression of information are essential for controlling the growing number of high-resolution photographs. The performance of compression techniques is assessed in this work using a deductive methodology employing a descriptive design, which is based on the interpretivist philosophy. For thorough analysis, secondary data gathering from several medical picture datasets is used. The study looks into well-known compression methodologies such wavelet-based methodologies, predictive computer programming, along with deep learning-based strategies. The results show wide variability in compression metrics, with wavelet-based techniques showing excellent spatial redundancies reduction performance. The tight equilibrium among compression overall diagnostic precision is highlighted by the slight artifacts introduced by some methods. The examination of computational resources reveals trade-offs between computing speed and memory needs, guiding real-world implementation. Statistical comparison highlights algorithmic differences and offers fact-based conclusions. The use of deep learning integration, specialized algorithm improvement, and dynamic compression methods are suggested. Future studies on telemedicine applications should investigate real-time compressing and hybrid methodologies. Data privacy and security must continue to be guided by moral and legal principles. With implications for better storage and availability for health care providers, this study enhances the field by providing an in-depth comprehension of compression algorithms within stored in the cloud medical images.