The storage of medical images is one of the challenges in the medical imaging field. There are variable works that use implicit neural representation (INR) to compress volumetric medical images. However, there is room to improve the compression rate for volumetric medical images. Most of the INR techniques need a huge amount of GPU memory and a long training time for high-quality medical volume rendering. In this paper, we present a novel implicit neural representation to compress volume data using our proposed architecture, that is, the Lanczos downsampling scheme, SIREN deep network, and SRDenseNet high-resolution scheme. Our architecture can effectively reduce training time, and gain a high compression rate while retaining the final rendering quality. Moreover, it can save GPU memory in comparison with the existing works. The experiments show that the quality of reconstructed images and training speed using our architecture is higher than current works which use the SIREN only. Besides, the GPU memory cost is evidently decreased.