Irregular grid tensor completion

TitleIrregular grid tensor completion
Publication TypeConference
Year of Publication2015
AuthorsCurt Da Silva, Felix J. Herrmann
Conference NameWorkshop on Low-rank Optimization and Applications
Month06
Keywordshierarchical tucker, irregular sampling, off the grid, structured tensor, tensor interpolation
Abstract

Low rank tensor completion has recently garnered the attention of researchers owing to the ubiquity of tensors in the sciences and the theoretical and numerical challenges compared to matrix completion. Here we consider a tensor completion scheme where the data arises from sampling a continuous function. When the sampling grid is not periodic, the resulting tensor may not be low rank in the Hierarchical Tucker sense, which can adversely affect reconstruction quality when there are missing samples. In order to compensate for this off-grid sampling, we introduce a resampling operator (here, the non-uniform Fourier transform) that accounts for this non-uniformity moreso than merely treating the sampling grid as periodic. Numerical experiments demonstrate that this approach can improve reconstruction quality when there is relatively little data.

Notes

(Workshop on Low-rank Optimization and Applications, University of Bonn, Germany)

Presentation

https://www.slim.eos.ubc.ca/Publications/Public/Conferences/WS_LR/2015/d...

Citation Keydasilva2015WSLRigt