The main contribution of this thesis is a new method of image compression based on a recently developed adaptive transform called Mixtures of Principal Components (MPC). Our multi-resolution extension of MPC-called Multi-Resolution Mixtures of Principal Components (MR-MPC) compresses and decompresses images in stages. The first stage processes the original images at very low resolution and is followed by stages that process the encoding errors of the previous stages at incrementally higher resolutions. To evaluate our multi-resolution extension of MPC we compared it with MPC and with the excellent performing wavelet based scheme called SPIHT. Fifty chest radiographs were compressed and compared to originals in two ways. First, Peak Signal to Noise Ratio (PSNR) and five distortion factors from a perceptual distortion measure called PQS were used to demonstrate that our multi-resolution extension of MPC can achieve rate distortion performance that is 220% to 720% better than MPC and much closer to that of SPIHT. And second, in a study involving 724 radiologists' evaluations of compressed chest radiographs, we found that the impact of MR-MPC and SPIHT at 25:1, 50:1, 75:1 on subjective image quality scores was less than the difference of opinion between four radiologists. / Thesis / Master of Science (MS)