Traditionally, the only bounds on the performance of image coding systems have been obtained by assuming stationary statistical models of the image data. Such models are, however, known to be unrealistic for natural images. An alternative approach, which is based on the essential non-stationarity of images, has been developed. Based on the uncertainty principle, it can be applied to study the performance of both predictive and transform coders. The purpose of the paper is to develop this approach and show how it can lead to a better understanding of the essential constraints on coder design. After an explanation of the general principles and the theoretical development, examples will be given to show how coders with superior performance can be developed by taking account of these bounds.