In this paper, a natural image compression method is proposed based on independent component analysis (ICA) and visual saliency detection. The proposed compression method learns basis functions trained from data using ICA to transform the image at first; and then sets percentage of the zero coefficient number in the total transforming coefficients. After that, transforming coefficients are sparser which indicates further improving of compression ratio. Next, the compression method performance is compared with the discrete cosine transform (DCT). Evaluation through both the usual PSNR and Structural Similarity Index (SSIM) measurements showed that proposed compression method is more robust to DCT. And finally, we proposed a visual saliency detection method to detect automatically the important region of image which is not or low compressed while the other regions are highly compressed. Experiment shows that the method can guarantee the quality of important region effectively.