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 language||English (US)|
|Title of host publication||2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||5|
|State||Published - May 2019|
|Event||44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom|
Duration: May 12 2019 → May 17 2019
|Name||ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings|
|Conference||44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019|
|Period||5/12/19 → 5/17/19|
Bibliographical noteFunding Information:
Supported in part by U.S. NSF grants IIS-1447788
Supported in part by U.S. NSF grants IIS-1447788, IIS-1704074, ECCS 1808159 and CCF-1651825, and NIH grant P41EB015894.
© 2019 IEEE.
- MRI acceleration
- functional MRI
- tensor completion