A design issue in remote visualization is on the mapping of the viewer’s intention to the relevant data to be sent. One possible approach is to let the viewer interactively indicate the region of interests (ROI), and objects in the ROI will have higher priority during transmission. For media objects like images and video, foveation has been used to formulate the priority of spatial information. Foveation can be treated as a way to distribute information across the space, in order to have wide coverage and yet high concentration in the interesting location. There are a number of works on image transmission and video encing exploiting the compression rate provided by foveation [Basu et 1993; Basu and Wiebe 1998; Chang et al. 20001. From another perspective, foveation can be viewed as a way to distribute computing resources across space. For example, Levoy et [Levoy and Whitaker propose to use foveation to speed up volume rendering. In this paper, we presented a novel algorithm for fast rendering volumes with special structure: foveated volumes. Our major contribution is to exploit the implicit structure of the foveated volume, different from other types of data, t o accelerate the volume rendering. We render a foveated volume directly in the Wavelet domain, and its running time depends mainly on the number of relevant coefficients. Potentially, foveation can be exploited in remote volume visualization to give a fast rendering that does not depend on the size of the full resolution volume.