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A novel multiresolution algorithm for lossy gray-scale image compression is presented. High-quality low bit rate image compression is achieved first by segmenting an image into regions of different sizes based on perceptual variation in each region and then constructing a distinct code for each block by using the theory of projection pursuit (PP). Projection pursuit allows one to adaptively construct a better approximation for each block by optimally selecting basis functions. The process is stopped when the desired peak signal-to-noise ratio (PSNR) or bit rate (b/pixel) is achieved. At rates below 0.5 b/pixel, our algorithm shows superior performance, both in terms of PSNR and subjective image quality, over the Joint Photographers Expert Group (JPEG) algorithm, and comparable performance to the embedded zerotree wavelet (EZW) algorithm.