Advanced methodologies for transmitting compressed images, within acceptable ranges of transmission rate and loss of information, make it possible to transmit a medical image through a communication channel. Most prior works on 3D medical image compression consider volumetric images as a whole but fail to account for the spatial and temporal coherence of adjacent slices. In this paper, we set out to develop a 3D medical image compression method that extends the 3D wavelet difference reduction algorithm by computing the similarity of the pixels in adjacent slices and progressively compress only the similar slices. The proposed method achieves high-efficiency performance on publicly available datasets of MRI scans by achieving compression down to one bit per voxel with PSNR and SSIM up to 52:3 dB and 0:7578, respectively.