Today, in the era of big data, an increasingly serious problem is the security of digital media in the healthcare domain. Encryption is a popular technique to resolve the security concern of medical data. In the paper, the authors propose a key-based encryption algorithm – namely, SeMIE, designed by RDWT and RSVD for healthcare applications – which can guarantee the security of the medical images. Initially, the image normalisation procedure along with RDWT-RSVD is followed to generate hash value. Here, image normalisation is used to ensure the high resistance against the geometric modifications. Then, a key expansion process is utilised with the hash value for generating the secure keys. Finally, the encryption process uses Feistel structure along with constant substitution-permutation functions to provide sufficient confusion and diffusion of cipher data. Experimental evaluation indicates that the SeMIE algorithm is secure against several attacks. From the simulation findings, it is inferred that the algorithm exhibits improved security compared to existing methods.