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Image compression using wavelet transform results in an improved compression ratio as well as image quality. Wavelet transform is the only method that provides both spatial and frequency domain information. These properties of wavelet transform greatly help in identification and selection of significant and nonsignificant coefficients amongst the wavelet coefficients. In this paper, we present a wavelet based image compression system using mathematical morphology and self organizing feature map (MMSOFM). The significance map is preprocessed using mathematical morphology operators to identify and create clusters of significant coefficients. A self-organizing feature map (SOFM) is then utilized to encode the significance map. Experimental results and comparisons with the JPEG are made to emphasize the results of this compression system.