Ensuring the security of medical imaging has garnered increasing attention in recent years; this interest comes within the context of smart healthcare systems. On the one hand, different encryption methods can be taken into consideration. Nevertheless, most of them have been designed for execution on PCs that suffer from serious disadvantages such as portability limitations, high energy consumption, and high costs. In order to overcome such limitations, hardware approaches have become in focus, offering real-time processing and enhanced security along with energy-efficient performance using embedded platforms and parallel computing architectures. We hereby contribute a novel and optimized compression-encryption scheme specifically designed for execution on Raspberry Pi. The proposed approach integrates three complementary phases: (1) image compression using discrete orthogonal Hahn moments for compact and faithful representation; (2) the encryption is based on a 4-D hyper-chaotic memristor system, a modified logistic map, and DNA encoding to offer strong defense against a variety of threats and a high degree of security; and (3) in addition, an optimization algorithm, namely Chaotic Archimedes Optimization Algorithm (CAO), is used to dynamically minimize the correlation between encrypted and original data. The design of this architecture provides a very secure, real-time process and low energy cost; therefore, it is an applicable and scalable solution for secure medical image transmission and storage in embedded and mobile health systems.