Comparing the 64x64 images with the original 256x256 version:
Discrete Wavelet Transform
All three methods give a good representation of the original. The Pixel Averaged image is fuzzier than the other two, and the DWT image preserves the details (such as the edges of the glasses and the lock of hair on her forehead) better than the other two. This is especially obvious if the images are expanded back to the original size.