In this thesis, an adaptive compression scheme based on the wavelet transform is implemented for grayscale images. The wavelet packet decomposition of the input image is performed, and from this, a best adapted wavelet packet tree is determined. A technique for representing this tree using a bitstring is proposed. This string is included in the output stream, for reconstruction of the image. The coefficients of the transform are vector quantized and written to the output stream. The method is compared with other wavelet based compression techniques and is found to have comparable performance in terms of compression ratio and quality of the reconstructed image.