For few decades digital X-ray imaging has been one of the most important tools for medical diagnosis. With the advent of distance medicine and the use of big data in this respect, the need for efficient storage and online transmission of these images is becoming an essential feature. Limited storage space and limited transmission bandwidth are the main challenges. Efficient image compression methods are lossy while the information of medical images should be preserved with no change. Hence, lossless compression methods are necessary for this purpose. In this paper, a novel method has been proposed to eliminate the non-ROI data from bone X-ray images. Background pixels do not contain any valuable medical information. The proposed method is based on the histogram dispersion method. ROI is separated from the background and it is compressed with a lossless compression method to preserve medical information of the image. Compression ratios of the implemented results show that the proposed algorithm is capable of effective reduction of the statistical and spatial redundancies.