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In order to apply the results of information theory to the efficient storage or transmission of images, it is necessary to model the image source distribution and specify an appropriate fidelity criterion. One useful source model results from separating the log intensity random field of a typical image into the sum of two nearly independent random fields with a simpler description. It has also been found that under certain conditions a frequency-weighted squared-error fidelity criterion is satisfactory for evaluating the images. Thus it is important to consider the situation in which the source output is the sum of two independent random entities with known rate-distortion functions with respect to a (perhaps frequency-weighted) squared-error criterion. These rate-distortion functions are used to provide new bounds to the rate-distortion function of the additive source with respect to the same criterion. In one example considered, the new bounds are the tightest known in certain distortion regions. Examples from image coding are given, including a comparison of the performances of various encoding schemes.