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We investigate analysis/synthesis systems for progressive-to-lossless embedded wavelet image coding. We propose a system which does not use an inverse lossless wavelet transform (ILWT) but an inverse wavelet transform (IWT). In this system, we must correct the mean value of rounding errors of each band. We also investigate a mixed-type system which is obtained by applying repeatedly a 4-band non-separable forward lossless wavelet transform (FLWT) for the lowest frequency band. Our simulation shows that the PSNR of the reconstructed image of the non-separable FLWT followed by the IWT is 2.7 dB higher than that of the separable FLWT followed by the ILWT at a bit rate, and that the mixed-type system switching inverse transforms depending on the bit rate has good performance at all bit rates.