The paper describe approach to the image compression using new hybrid Transforms ,namely, the improvement ridgelet transform that has proven to show promising results over ridgelet transform. The hybrid transform based of replacing the wavelet transform with the slantlet transform, the slantlet transform is a discrete wavelet transform with two zero moments and with improved time localization. A comparison was made with compression using ridgelet transform for different images. A high quality image compression has been achieved for natural images. Computer simulation results indicate that the improvement ridgelet transform offers superior and faster compression performance compared to the ridgelet transform based approaches.