In this paper, CS based medical images compression framework has been presented. The discrete cosine transform (DCT) as well as discrete wavelet transform (DWT) have been used for finding the sparsity in the medical images. The comparison of the results obtained by combining DCT and DWT with CS for medical images-CT and MRI-has been presented.The CS & DWT compression scheme achieved a maximum compression ratio (CR) of 3.01 with PSNR of 31.6732 dB and average CoC value of 0.9983 for an MRI image, whereas for CT image these values are 2.89, 31.7935 dB and 0.9987, respectively.The CS and DCT based algorithm could obtain a maximum CR value of 1.5789 with average values (for both types of images) of PSNR, RMSE and CoC of 13.1774 dB, 56.0007 and 0.8384, respectively.