Hierarchical and wavelet-based multilinear models for multi-dimensional visual data approximation

With advances in imaging technologies such as CCD, laser, magnetic resonance, and diffusion tensor; visual data of multiple dimensions have been produced at an unprecedented rate and scale. These new technologies bring new challenges to existing multidimensional image compression techniques. In ["Hierarchical tensor approximation of multidimensional images" and "Hierarchical tensor approximation of multidimensional visual data" by Q. Wu et. al.] we exploit the aforementioned characteristics of visual data and develop a compact representation technique based on a hierarchical tensor based transformation. In this technique, an original multidimensional dataset is transformed into a hierarchy of signals to expose its multiscale structures. In ["Wavelet based hybrid multilinear models for multidimensional image approximation" by Q. Wu et. al.] we propose hybrid multilinear models in the wavelet domain to harness the power of both wavelet (packet) transforms and tensor approximation.