In this Book Image compression using Fast DCT and fast DWT based on different wavelet families for various sizes of image frame at varying decomposition level is studied. The experiments revealed that compression of the image signals without significant degradation of the visual quality is possible as they contain a high degree of redundant information not perceived by the other image compression techniques.The removal procedure is achieved via the most common techniques: the DCT and the DWT. These techniques are tested on the various test image The noticeable blocking artifacts inherent in the DCT based reconstructed images vanish in the DWT based reconstructions without sacrificing the visual quality. Especially the images reconstructed from the deeper wavelet decomposition levels have higher PSNRs. a comparative study of different wavelet family with fast cosine transform (2D-DCT) on to own test images set has been done using MSE, PSNR and compression ratio (CR).