Regular Sampling of Tensor Signals: Theory and Application to FMRI

Charilaos I. Kanatsoulis, Nicholas D. Sidiropoulos, Mehmet Akcakaya, And Xiao Fu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Sampling lies at the heart of signal processing. The celebrated Shan-non - Nyquist theorem states that in order to reconstruct a continuous or discrete time signal from uniform samples one must sample at a rate twice the highest frequency present in the signal. Numerous signals and images of interest, however, are not even approximately bandlimited. While much progress has happened in recent years, reconstruction from sub-Nyquist samples still hinges on the use of random / incoherent (aggregate) sampling patterns, instead of uniform or regular sampling, which is far more simple, practical, and natural in many applications. In this work, we study regular sampling and reconstruction of three- or higher-dimensional signals (tensors). We prove that exact tensor reconstruction from regular samples is feasible under mild conditions on the rank of the tensor. Furthermore we cast the functional magnetic resonance imaging (fMRI) acceleration task as a regular tensor sampling problem and provide an algorithmic framework that effectively handles the reconstruction task. Experiments based on synthetic data and real fMRI data showcase the effectiveness of our approach.

Original languageEnglish (US)
Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2932-2936
Number of pages5
ISBN (Electronic)9781479981311
DOIs
StatePublished - May 2019
Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: May 12 2019May 17 2019

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2019-May
ISSN (Print)1520-6149

Conference

Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
CountryUnited Kingdom
CityBrighton
Period5/12/195/17/19

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Keywords

  • MRI acceleration
  • functional MRI
  • reconstruction
  • sampling
  • tensor completion

Cite this

Kanatsoulis, C. I., Sidiropoulos, N. D., Akcakaya, M., & Fu, A. X. (2019). Regular Sampling of Tensor Signals: Theory and Application to FMRI. In 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings (pp. 2932-2936). [8682230] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2019-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2019.8682230