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An embedded lossy-to-lossless coder for hyperspectral images is presented. The proposed coder couples a reversible integer-valued Karhunen-Loeve transform with an extension into 3-D of the tarp-based coding with classification for embedding (TCE) algorithm that was originally developed for lossy coding of 2-D images. The resulting coder obtains lossy-to-lossless operation while closely matching the lossy performance of JPEG2000. Additionally, for lossless compression, it consistently outperforms not only JPEG2000 but, often, several prominent purely lossless methods.