Volumetric data sets require enormous storage capacity even at moderate resolution levels. The excessive storage demands not only stress the capacity of the underlying storage and communications systems, but also seriously limit the speed of volume rendering due to data movement and manipulation. A novel volumetric data visualization scheme is proposed and implemented in this work that renders 2D images directly from compressed 3D data sets. The novelty of this algorithm is that rendering is performed on the compressed representation of the volumetric data without pre-decompression. As a result, the overheads associated with both data movement and rendering processing are significantly reduced. The proposed algorithm generalizes previously proposed whole-volume frequency- domain rendering schemes by first dividing the 3D data set into subcubes, transforming each subcube to a frequency-domain representation, and applying the Fourier Projection Theorem to produce the projected 2D images according to given viewing angles. Com- pared to the whole-volume approach, the subcube-based scheme not only achieves higher compression efficiency by exploiting local coherency, but also improves the quality of resultant rendering im- ages because it approximates the occlusion effect on a subcube by subcube basis.