Disclosed are methods and apparatus for prioritization of transform domain coefficient data representing sources such as, but not limited to, single images and images in motion, so as to produce a data rate not exceeding the capacity of the transmission channel used in transmitting the data to a receiver and to simultaneously minimize the perceived distortion when the image is reconstructed at the receiver. One disclosed aspect relates in particular to transmission of Pyramid Transform coefficients from a single image over a fixed data rate transmission channel. In effect a sequence of multiple image reconstructions is performed at the receiver during the time period required for the transmission of all of the coefficient data representing the image. The reconstructed image gradually increases in detail. Another disclosed aspect relates to the transmission of transform domain coefficients for an image which is undergoing change with time, and applies to any transform for which transform domain coefficients can be organized in a hierarchial manner in multiple bands, regardless of the manner in which the transform process actually proceeds. Identical transform coefficient models are maintained at both the transmitter and the receiver. The transmitter identifies transform coefficient changes necessary to cause a transform coefficient model to completely represent the most current image, prioritizes the change data, and selects a subset of said change data consistent with the limitation of a fixed rate transmission channel. Advantageous mapping and signalling techniques are disclosed for maintaining the coefficient models and for efficiently signalling the changes.