Storage and transmission of high-compression 3D radiological images that create high-quality reconstruction upon decompression are critical necessities for effective and efficient teleradiology. To cater to this need, we propose a near lossless 3D image volume compression method based on optimal multilinear singular value decomposition called "3D-VOI-OMLSVD." The proposed strategy first eliminates any blank 2D image slices from the 3D image volume and uses the selective bounding volume (SBV) to identify and extract the volume of Interest (VOI). Following this, the VOI is decomposed with an optimal multilinear singular value decomposition (OMLSVD) to obtain the corresponding core tensor, factor matrices, and singular values that are compressed with adaptive binary range coder (ABRC), integrated as an entropy encoder. The compressed file can be transferred or transmitted and then decompressed in order to reconstruct the original image. The resultant decompressed VOI is acquired by reversing the above process and then fusing it with the background, using the bound volume coordinates associated with the compressed 3D image. The proposed method performance was tested on a variety of 3D radiological images with different imaging modalities and dimensions using quantitative evaluation metrics such as the compression rate (CR), bit rate (BR), peak signal to noise ratio (PSNR), and structural similarity index (SSIM). Furthermore, we also investigate the impact of VOI extraction on the model performance, before comparing it with two popular compression methods, namely JPEG and JPEG2000. Our proposed method, 3D-VOI-OMLSVD, displayed a high CR value, with a maximum of 37.31, and a low BR, with the lowest reported to be 0.21. The SSIM score was consistently high, with an average performance of 0.9868, while using < 1 second for decoding the image. We observe that with VOI extraction, the compression rate increases manifold, and bit rate drops significantly, and thus reduces the encoding and decoding time to a great extent. Compared to JPEG and JPEG2000, our method consistently performs better in terms of higher CR and lower BR. The results indicate that the proposed compression methodology performs consistently to create high-quality image compressions, and overall gives a better outcome when compared against two state-of-the-art and widely used methods, JPEG and JPEG2000.