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We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue p ...
We present a framework based on convex optimization and spectral regularization to perform learning when feature observations are multidimensional arrays (tensors). We give a mathematical characterization of spectral penalties for tensors and analyze a uni ...
We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch and Lubich; see [SIAM J. Matrix Anal. Appl., 29 (2007), pp. 434-454], [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2360-2375]) to the re ...
Society for Industrial and Applied Mathematics2013
Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We review our previous work, which reformulates this nonlinear problem in the framework of tensor recover ...
For linear models, compressed sensing theory and methods enable recovery of sparse signals of interest from few measurements-in the order of the number of nonzero entries as opposed to the length of the signal of interest. Results of similar flavor have mo ...
Institute of Electrical and Electronics Engineers2012
The numerical solution of linear systems with certain tensor product structures is considered. Such structures arise, for example, from the finite element discretization of a linear PDE on a d-dimensional hypercube. Linear systems with tensor product struc ...
Society for Industrial and Applied Mathematics2009
Videos representing flames, water, smoke, etc. are often defined as dynamic textures: "textures" because they are characterized by redundant repetition of a pattern and "dynamic" because this repetition is also in time and not only in space. Dynamic textur ...
Institute of Electrical and Electronics Engineers2008
In nature, textures can be found everywhere. Texture, together with color and shape, represents the fundamental characteristics of objects. Texture conveys an idea of repetition of a certain structure, which is not limited only to the visual domain. We can ...