We propose a new image compression-decompression method that reproduces images with lower entropy (bit rates), particularly high-resolution images, than those processed by the DCT-based method at the same PSNR values. We predict each block by estimating the gradient, and then apply an orthogonal transformation to the prediction error. Our method is based on the Haar transform that requires only O(N) operations for an input signal of length N while the DCT requires O(N log2 N) operations. This advantage is particularly significant for images with a high-resolution. Our numerical experiments using 2048 × 2048 resolution images demonstrate the superiority of the proposed method over the DCT-based one.