Tensor Completion from Regular Sub-Nyquist Samples

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; from the system design point of view, it is far simpler to implement, and often necessary due to system constraints.

In this webinar, the presenters study regular sampling and reconstruction of three- or higher dimensional signals (tensors). They 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, they show that functional magnetic resonance imaging (fMRI) acceleration is a tensor sampling problem, where design of practical sampling schemes and an algorithmic framework are used to handle it. Numerical results show that their tensor sampling strategy accelerates the fMRI sampling process significantly without sacrificing reconstruction accuracy.