Sparse Sampling for Inverse Problems with Tensors
Guillermo Ortiz-Jimenez (Student TU Delft, École Polytechnique Fédérale de Lausanne)
Mario Coutiño (TU Delft - Signal Processing Systems)
Sundeep Prabhakar Chepuri (Indian Institute of Science, TU Delft - Signal Processing Systems)
GJT Leus (TU Delft - Signal Processing Systems)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
Abstract
We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop low-complexity greedy algorithms based on submodular optimization methods to compute near-optimal sampling sets. We present several numerical examples, ranging from multiantenna communications to graph signal processing, to validate the developed theory.