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An image compression algorithm has been developed that is well-suited to astronomical images. The method has 3 steps: an intensity mapping to generate an image that has roughly constant noise in each pixel, an orthonormal wavelet transform, and quadtree coding of the bit-planes of the wavelet coefficients. The quadtree values may be further compressed by any standard compression technique, such as Huffman or arithmetic coding. If the 2-dimensional Haar transform is used, the calculations can be carried out using integer arithmetic, and the method can be used for both lossy and lossless compression. The Haar transform basis functions are well-suited to most astronomical images because they are highly localized. The performance of the algorithm using smoother, longer range wavelets has also been explored; they can give slightly better lossy compression at the cost of an increase in artifacts around point sources, but they are not effective for lossless compression using this scheme. The algorithm using Haar transforms is being used for compression of the STScI Digitized Sky Survey now being distributed on CD-ROMs.
This technique has been used as the basis of a progressive image transmission system that can be used for either remote observing or access to remote image archives. After less than 1\% of the data have been received, the image is visually similar to the original, so it is possible to assess the quality of images very quickly. If necessary, the entire compressed data set can be sent so that the original image is recovered exactly. J.~Percival describes the remote observing system in an accompanying paper.
