Advanced 3D microstructural analysis in natural sciences and engineering depends ever more on modern data acquisition and imaging technologies such as micro-computed or synchrotron tomography and interactive visualization. The acquired volume data sets are not only of high-resolution but in particular exhibit complex spatial structures at different levels of scale (e.g. variable spatial expression of multiscale periodic growth structures in tooth enamel). Such highly structured volume data sets represent a tough challenge to be analyzed and explored by means of interactive visualization due to the amount of raw volume data to be processed and filtered for the desired features. As an approach to address this bottleneck by multiscale feature preserving data reduction, we propose higher-order tensor approximations (TAs). We demonstrate the power of TA to represent, and highlight the structural features in volume data. We visually and quantitatively show that TA yields high data reduction and that TA preserves volume features at multiple scales.