The increased popularity of multimedia applications places a great demand on efficient data storage and transmission techniques. Some methods have been proposed to combine compression and encryption together to reduce the overall processing time, but they are either insecure or intensive computationally. specially, they are unsuitable to wireless communication of mobile device. We propose a novel solution called partial encryption, We introduce quadtree and zerotree wavelet image compression in this paper, it reduces computation for date transmission in mobile device, and does not reduce the compression rate. In conclusion, the proposed partial encryption schemes are fast, secure, and do not reduce the compression performance of underlying compression algorithm.