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Transform coding proves to be efficient and practical for image compression. A three-dimensional reversible integer lapped transform (3D-RLT) is presented. Moreover, based on 3D-RLT, a progressive lossy-to-lossless compression algorithm is proposed for hyperspectral images. Experimental results demonstrate that the 3D-RLT performs better than a 3D 9/7 wavelet transform (3D-9/7WT) at most bit rates in lossy compression, and achieves competitive lossless compression performance compared with a 3D integer 5/3WT.