In current days, Digital Imaging and Communication in Medicine (DICOM) is widely used for viewing medical images from different modalities, distribution and storage. Image processing can be processed by photographic, optical and electronic means, because digital methods are precise, fast and flexible, image processing using digital computers are the most common method. Image Processing can extract information, modify pictures to improves and change their structure (image editing, composition and image compression etc.). Image compression is the major entities of storage system and communication which is capable of crippling disadvantages of data transmission and image storage and also capable of reducing the data redundancy. Medical images are require to stored for future reference of the patients and their hospital findings hence, the medical image need to undergo the process of compression before storing it. Medical images are much important in the field of medicine, all these Medical image compression is necessary for huge database storage in Medical Centre and medical data transfer for the purpose of diagnosis. Presently Discrete cosine transforms (DCT), Run Length Encoding Lossless compression technique, Wavelet transforms (DWT), are the most usefully and wider accepted approach for the purpose of compression. On basis of based on discrete wavelet transform we present a new DICOM based lossless image compression method. In the proposed method, each DICOM image stored in the data set is compressed on the basis of vertically, horizontally and diagonally compression. We analyze the results from our study of all the DICOM images in the data set using two quality measures namely PSNR and RMSE. The performance and comparison was made over each images stored in the set of data set of DICOM images. This work is presenting the performance comparison between input images (without compression) and after compression results for each images in the data set using DWT method. Further the performance of DWT method with HAAR process is compared with 2D-DWT method using the quality metrics of PSNR & RMSE. The performance of these methods for image compression has been simulated using MATLAB.