Medical imaging is an important source of digital information to diagnose the illness of a patient. The digital information generated consists of different modalities that occupy more disk space, and the distribution of the data occupies more bandwidth. A digital image compression technique that can reduce an image's size without losing much of its important information is challenging. In this paper, a novel image compression technique based on BPN and Arithmetic coders is proposed. The high non-linearity and unpredictiveness of the interrelationship between the pixels present in the image to be compressed is handled by BPN. An efficient coding technique called Arithmetic coding is used to produce an image with a better compression ratio and lower redundancy. A deep CNN based image deblocker is used as a post-processing step to remove the artefacts present in the reconstructed image to improve the quality of the reconstructed image. The effectiveness of the proposed methodology is validated in terms of PSNR. The proposed method is able to achieve about a 3% improvement in PSNR compared with the existing methods.