The use of multimedia communication has grown significantly in recent years, which has raised demand for image data compression. One popular technique for representing an image in an efficient format is image compression. It results in low rates of transmission by precisely lowering the number of bits required to store the images. Since medical image data is growing so quickly, there is a lot of research being done on how to upload and store large amounts of medical images in real time while having a limited amount of storage space and network bandwidth. But still, at this time, medical image compression technology is unable to optimize both rate and distortion. The goal of the proposed hybrid compression technique is to increase compression performance without losing the standard of the image. Even though they need a lot of storage, 3D medical images provide detailed information about disease. Optimal Multi-linear Singular Value Decomposition (OMLSVD) and deep auto-encoders are used in the current work to compress 3D healthcare images. The Federated Learning technique addresses the issues of data privacy and leakage by having each user train a model on its dataset before sending the model's local weights to a global federated server. So, use a federated server to get a global dataset weight without leaking or publishing datasets, protecting privacy. The quality of 3D compression images can be improved by using the proposed Hybrid approach. Experimental evaluation demonstrates SSIM values near 1 and high PSNR, indicating excellent reconstruction quality. Additionally, it compares the image with the compressed JPEG2000 and the proposed Hybrid approach. Since the images have different storage sizes, they all appear to be identical.