Compression of digital images has been a topic of research for many years and a number of image compression standards have been created for different applications. This thesis focuses on some key technologies for image compression, namely wavelet-based image coders that combines transform coding with sub-band coders and carried out a comparative study of wavelet-based coding for still images using second generation wavelets via lifting scheme. Wavelet coders apart from offering superior compression ratios have also very useful features such as resolution scalability. There has been recent interest in building reversible integer transforms using lifting scheme for image compression. These transforms allow both lossless and lossy decoding-by resolution or accuracy- using a single bit stream.By integrating lossy and lossless compression in a natural fashion, a single image compression method provides excellent lossy performance as well as supporting many applications that require the ability to exactly recover the original image.