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The problem of progressive lossless image coding is addressed. A nonlinear decomposition for progressive lossless compression is presented. The decomposition into subbands is called rank-order polynomial decomposition (ROPD) according to the polynomial prediction models used. The decomposition method presented here is a further development and generalization of the morphological subband decomposition (MSD) introduced earlier by the same research group. It is shown that ROPD provides similar or slightly better results than the compared coding schemes such as the codec based on set partitioning in hierarchical trees (SPIHT) and the codec based on wavelet/trellis-coded quantization (WTCQ). The authors' proposed method highly outperforms the standard JPEG. The proposed lossless compression scheme has the functionality of having a completely embedded bit stream, which allows for data browsing. It is shown that the ROPD has a better lossless rate than the MSD but it has also a much better browsing quality when only a part of the bit stream is decompressed. Finally, the possibility of hybrid lossy/lossless compression is presented using ultrasound images. As with other compression algorithms, considerable gain can be obtained if only the regions of interest are compressed losslessly.