This study addresses some mathematical and statistical techniques of medical image compression and their computational implementation. Fundamental theories have been presented, applied and illustrated with examples. To make the report as self-contained as possible, key terminologies have been defined and some classical results and theorems are stated, in the most part, without proof. Some algorithms and techniques of image processing have been described and substantiated with experimentation using MATLAB. Medical image compression is necessary for huge database storage in Medical Centers and medical data transfer for the purpose of diagnosis. Wavelet transforms present one such approach for the purpose of compression. The same has been explored in study with respect to wide variety of medical images. In this approach, the redundancy of the medical image and DWT coefficients are reduced through thresholding and further through Huffman encoding. In this study our main goal is to compare different types of wavelets for medical image compression. Finally, implementation of the above-mentioned concepts is illustrated.