Image compression using transform coding technique has been widely used in practice. However, 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 non-significant coefficients from amongst the wavelet coefficients. Wavelet transform based image compression result in an improved compression ratio as well as image quality and thus both the signficant coefficients and their positions within an image are encoded and transmitted. In this thesis a wavelet based image compression system is presented that uses mathematical morphology and self organizing feature map (MMSOFM). The significance map is preprocessed using mathematical morphology operators to identify and creat clusters of significant coefficients. A self-organizing feature map (SOFM) is then used to encode the significance map. Experimental results are shown and comparisons with JPEG and JPEG 2000 are made to emphasize the results of this compression system.