Hierarchical Tensor Approximation of Multidimensional Images

Abstract

Visual data comprises of multi-scale and inhomogeneous signals. In this paper, we exploit these characteristics and develop an adaptive data approximation technique based on a hierarchical tensor-based transformation. In this technique, an original multi-dimensional image 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 collective tensor approximation technique. Experimental results indicate that our technique can achieve higher compression ratios than existing functional approximation methods, including wavelet transforms, wavelet packet transforms and single-level tensor approximation.