Image compression is a demanding research area in the field of visual communication, in entertainment, medical and business applications. A new method is proposed using unsupervised learning neural networks and wavelet transformations, since the wavelet transformation uses subband decomposition of an image, it provides enhanced picture quality at higher compression ratios, Also our new algorithm avoids blocking artifacts. In this paper, the performances of haar and DB2 wavelet family are compared with MSE and PSNR. The experiment was carried out with .jpeg images. It is a good reference for application developers to select a good wavelet transformation system.