Sparse Sampling for Inverse Problems with Tensors

Guillermo Ortiz-Jimenez, Mario Coutino, Sundeep Prabhakar Chepuri, Geert Leus

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Article number8705331
Pages (from-to)3272-3286
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume67
Issue number12
DOIs
Publication statusPublished - 2019

Keywords

  • Graph signal processing
  • multidimensional sampling
  • sparse sampling
  • submodular optimization
  • tensors

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