Sparse Sampling for Inverse Problems with Tensors
arXiv:1806.10976 · doi:10.1109/TSP.2019.2914879
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 multi-antenna communications to graph signal processing, to validate the developed theory.
13 pages, 7 figures