Diagnostic quality medical images consume vast amounts of network time, system bandwidth and disk storage in current computer architectures. There are many ways in which the use of system and network resources may be optimize without compromising diagnostic image quality. One of these is in the choice of image representation, both for storage and transfer. In this paper, we show how a particularly flexible method of image representation, based on Mallat's algorithm, leads to efficient methods of both lossy image compression and progressive image transmission. We illustrate the application of a progressive transmission scheme to medical images, and provide some examples of image refinement in a multiscale fashion. We show how thumbnail images created by a multiscale orthogonal decomposition can be optimally interpolated, in a minimum square error sense, based on a generalized Moore-Penrose inverse operator. In the final part of this paper, we show that the representation can provide a framework for lossy image compression, with signal/noise ratios far superior to those provided by a standard JPEG algorithm. The approach can also accommodate precision based progressive coding. We show the results of increasing the priority of encoding a selected region of interest in a bit-stream describing a multiresolution image representation.