The compression of 3-D digital images, such as those obtained from Magnetic Resonance Imaging or Computed Tomography, makes it possible to save and transmit data sets in less space and time. Although there is a trade off between compression and resolution, it is believed that a substantial decrease in the number of voxels, volume elements, will not noticeably degrade the 3-D image. As a result, to the clinician, the efficacy of the image will not be changed, but the amount of bytes needed to represent the image will be decreased. A multiresolution image representation is used as a basis for constructing an approximation the original image, and this method is based on 3-dimensional, separable splines. A multiresolution algorithm is being developed that computes the solution to the approximation problem in O(log N), on a single-instruction, multiple-data architecture, SIMD. SIMD is a fine grain parallel architecture and N is the number of voxels in the original image.