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Hierarchical Tensor Approximation of Multi-Dimensional Visual Data
January/February 2008 (vol. 14 no. 1)
pp. 186-199

Abstract—Visual data comprise of multi-scale and inhomogeneous signals. In this paper, we exploit these characteristics and develop a compact data representation technique based on a hierarchical tensor-based transformation. In this technique, an original multi-dimensional dataset is transformed into a hierarchy of signals to expose its multi-scale structures. The signal at each level of the hierarchy is further divided into a number of smaller tensors to expose its spatially inhomogeneous structures. These smaller tensors are further transformed and pruned using a tensor approximation technique. Our hierarchical tensor approximation supports progressive transmission and partial decompression. Experimental results indicate that our technique can achieve higher compression ratios and quality than previous methods, including wavelet transforms, wavelet packet transforms, and single-level tensor approximation. We have successfully applied our technique to multiple tasks involving multi-dimensional visual data, including medical and scientific data visualization, data-driven rendering and texture synthesis.

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Index Terms:
Multilinear Models, Multidimensional Image Compression, Hierarchical Transformation, Tensor Ensemble Approximation, Progressive Transmission, Texture Synthesis
Qing Wu, Tian Xia, Chun Chen, Hsueh-Yi Sean Lin, Hongcheng Wang, Yizhou Yu, "Hierarchical Tensor Approximation of Multi-Dimensional Visual Data," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 1, pp. 186-199, Jan.-Feb. 2008, doi:10.1109/TVCG.2007.70406
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