Tensor Completion from Regular Sub-Nyquist Samples

You are here

Top Reasons to Join SPS Today!

1. IEEE Signal Processing Magazine
2. Signal Processing Digital Library*
3. Inside Signal Processing Newsletter
4. SPS Resource Center
5. Career advancement & recognition
6. Discounts on conferences and publications
7. Professional networking
8. Communities for students, young professionals, and women
9. Volunteer opportunities
10. Coming soon! PDH/CEU credits
Click here to learn more.

Tensor Completion from Regular Sub-Nyquist Samples

By: 
Charilaos I. Kanatsoulis; Xiao Fu; Nicholas D. Sidiropoulos; Mehmet Akçakaya

Signal sampling and reconstruction is a fundamental engineering task at the heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees perfect signal reconstruction from uniform samples, obtained at a rate twice the maximum frequency present in the signal. Unfortunately a large number of signals of interest are far from being band-limited. This motivated research on reconstruction from sub-Nyquist samples, which mainly hinges on the use of random/incoherent sampling procedures. However, uniform or regular sampling is more appealing in practice and from the system design point of view, as it is far simpler to implement, and often necessary due to system constraints. In this work, we study regular sampling and reconstruction of three- or higher-dimensional signals (tensors). We show that reconstructing a tensor signal from regular samples is feasible. Under the proposed framework, the sample complexity is determined by the tensor rank-rather than the signal bandwidth. This result offers new perspectives for designing practical regular sampling patterns and systems for signals that are naturally tensors, e.g., images and video. For a concrete application, we show that functional magnetic resonance imaging (fMRI) acceleration is a tensor sampling problem, and design practical sampling schemes and an algorithmic framework to handle it. Numerical results show that our tensor sampling strategy accelerates the fMRI sampling process significantly without sacrificing reconstruction accuracy.

SPS on Twitter

SPS Videos


Signal Processing in Home Assistants

 


Multimedia Forensics


Careers in Signal Processing             

 


Under the Radar