In this paper, we present an efficient compression technique that is suitable for image/video communications over wireless (mobile) channel. Our technique uses basic directional differences operators to estimate corresponding detail subband images/videos from their approximation subband images/videos. We empirically found that the detail subband images/videos can be well approximated by the estimate subband images/videos. In this work, image and video are first decomposed using integer wavelet packet transformation. Having established that detail subband images/video can be estimated from the approximation subbands, the information needed to send over the wireless channel is only the most important subband images/video, where we selected them via best basis selection algorithm. Next, after best basis selection, the selection subband components are encoded using either SPIHT (JPEG) for image or 3-D SPIHT for video and then the encoded data are sent over the wireless channel. The advantages of our algorithms are two folds. First, most of the computation used in our technique is performed in integer for the purpose of coding speed improvement. Second, the computation of our algorithm (either SPIHT (JPEG) or 3-D SPIHT) is reduced from its original computation by an order of magnitude. The reason is that in our algorithm either SPIHT (JPEG) or 3-D SPIHT is performed only on the set of important components (two or a few subband image/videos) instead of the whole image/video. Finally, we show that our proposed algorithm using SPIHT (3-D SPIHT) are better that pure JPEG (MPEG-2) both in terms of human visual image and computation complexity.