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We present a novel and fast algorithm to compress an image using nonlinear wavelets under a nonexpansive image pyramid framework. An image pyramid is constructed by downsampling the image and by computing the difference pyramid by upsampling a lower resolution image to predict the next higher resolution image. The novelty of the method lies in using a nonlinear adaptive method to upsample the image, and in processing of the prediction difference in order to reduce its entropy. Performance of the lossless compression is comparable or only slightly worse than the best lossless compression algorithms such as CALIC and LOCO-I, and it also has the additional feature of multiresolution format. The algorithm also works well in lossy mode and it has superior performance on mixed text/graphics images than SPIHT and JPEG.