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In this study, the history of the development of wavelet transform is reviewed, and a discussion is presented on the implementation issues for wavelet transforms. The four main coding methods for image compression using wavelet transforms are studied in detail. More importantly the factors that affect coding efficiency are identified. The main contribution of this research is the introduction of a new low-complexity coding algorithm for image compression based on wavelet transforms. The algorithm is based on block dividing coding (BDC) with an optimised packet assembly. Our extensive simulation results show that the proposed algorithm outperforms JPEG2000 in lossless coding, even though it still leaves a narrow gap in lossy coding situations.