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We propose novel algorithms for stereoscopic image coding based on the hierarchical decomposition of stereo information. The proposed schemes, based on the wavelet transform and zerotree quantization, are endowed with excellent progressive transmission capability and retain the option for perfect reconstruction of the original image pair. Experimental evaluation shows that the resulting methods produce superior results when compared with other algorithms for stereo image coding. This is achieved without introducing blocking artifacts and with the valuable additional convenience of the production of embedded bitstreams.