If this is the case then the whole tree can be coded with a single zerotree symbol. Now if the image is scanned in a predefined order, going from high scale to low, implicitly many positions are coded through the use of zerotree symbols. Of course the zerotree rule will be violated often, but as it turns out in practice, the probability is still very high in general. The price to pay is the addition of the zerotree symbol to our code alphabet. Now that we have all the terms defined we can start compressing.
Lets begin with the encoding of the coefficients in decreasing order.
A very direct approach is to simply transmit the values of the coefficients in decreasing order, but this is not very efficient. This way a lot of bits are spend on the coefficient values and we do not use the fact that we know that the coefficients are in decreasing order. A better approach is to use a threshold and only signal to the decoder if the values are larger or smaller than the threshold. If we also transmit the threshold to the decoder, it can reconstruct already quite a lot. To arrive at a perfect reconstruction we repeat the process after lowering the threshold, until the threshold has become smaller than the smallest coefficient we wanted to transmit.