Interactive visual analysis of large and complex volume datasets is an ongoing and challenging problem. We tackle this challenge in the context of state-of-the-art out-of-core multiresolution volume rendering by introducing a novel hierarchical tensor approximation (TA) volume visualization approach. The TA framework allows us (a) to use a rank-truncated basis for compact volume representation, (b) to visualize features at multiple scales, and (c) to visualize the data at multiple resolutions. In this paper, we exploit the special properties of the TA factor matrix bases and define a novel multiscale and multiresolution volume rendering hierarchy. Different from previous approaches, to represent one volume dataset we use but one set of global bases (TA factor matrices) to reconstruct at all resolution levels and feature scales. In particular, we propose a coupling of multiscalable feature visualization and multiresolution DVR through the properties of global TA bases. We demonstrate our novel TA multiresolution hierarchy based volume representation and visualization on a number of mCT volume datasets.