After one stage of averaging and differencing, in two directions, as explained in the preceding page, you can iterate the procedure: on the array that corresponds to averaging horizontally and vertically (top left in the example on the previous page), you can go for another round of averaging and differencing, and so on. The numbers you compute in this way are called wavelet coefficients for the image; the particular wavelet transform we have used is called the Haar wavelet transform: it consists of the simple averaging and differencing we have described above, except for an overall normalization factor.

On this page you can carry out a variety of experiments with this type of image compression. You can choose the number of levels (that is, the number of "rounds" of averaging and differencing), or how much you wish to round off the coefficients after they have been transformed; you can view the reconstruction after this rounding off. You can also replace the Haar transform with a more sophisticated wavelet transform, where the averages and differences are replaced by generalized averages and generalized differences; this will be called here the Smooth wavelet transform.

On the Control Panel below, you will get two columns, allowing you to set all the different choices independently for two images. This will enable you to carry out lots of comparisons.