Secure and efficient transmission of medical images requires integrating compression, encryption, and substitution mechanisms to protect sensitive patient data. Compression reduces image size, improving transmission and storage while preserving diagnostic quality. Encryption ensures confidentiality and the Health Insurance Portability and Accountability Act (HIPAA) compliance, safeguarding patient information from unauthorized access. Nonlinear substitution using dynamic S-boxes increases confusion and strengthens resistance to cryptanalysis. This paper presents a hybrid medical image encryption scheme comprising three sequential stages for high security and computational efficiency. In preprocessing, images are resized, normalized, partitioned into uniform blocks, and compressed using compressive sensing based on partial discrete Fourier transform sampling. The encryption stage applies adaptive S-boxes with block interleaving, followed by the Advanced Encryption Standard in Galois/Counter Mode to provide integrity-preserving encryption. During decryption, the Fast Iterative Shrinkage-Threshold Algorithm reconstructs images accurately. Experimental results demonstrate that the scheme preserves image quality, achieves effective compression, and resists statistical and cryptographic attacks, making it suitable for secure medical image communication in resource-limited environments.