Digital Imaging and Communications in Medicine (DICOM) is a standard image format for distribution and viewing of medical images from different modalities. For transmitting the medical images over the internet and for storing for future use, different compression techniques have been employed. This paper addressed most of the existing DICOM image compression techniques and studied the performance of the respective compression algorithms using visual inspection method and verified quantitatively in terms of compressed file size, compression ratio, PSNR and MSSIM.Finally, the optimum compression technique found from this study has been discussed in terms of the visual perception and performance metrics.