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In this paper a novel approach of information theory based minimum relative entropy (MRE) and entropy methods for image compression is discussed. A two stage compression process is performed through homogenous MRE method, and heterogeneous MRE. The compressed images are reconstructed through region growing techniques. A comparison of MRE with DCT is also studied for the compression ratio of 12. The performance of image compression and restoration is analyzed by the estimation of parametric values such as mean square error (MSE) and peak signal to noise ratio (PSNR). Higher the PSNR better the reconstruction process. Six radiographic medical images of various sizes and five ultrasonic images are analyzed. Higher PSNR of 33 dB is achieved in MRE method when compared to 32 dB in DCT. The results of soft decision tree method is also listed. It gives better result in the case of 512times512 images.