A super-resolution framework for tensor decomposition

Qiuwei Li, Ashley Prater, Lixin Shen, Gongguo Tang

Research output: Contribution to journalArticlepeer-review


This work considers a super-resolution framework forovercomplete tensor decomposition. Specifically, we view tensor decomposition as a super-resolution problem of recovering a sum of Dirac measures on the sphere and solve it by minimizing a continuous analog of the ℓ1 norm on the space of measures. The optimal value of this optimization defines the tensor nuclear norm. Similar to the separation condition in the super-resolution problem, by explicitly constructing a dual certificate, we develop incoherence conditions of the tensor factors so that they form the unique optimal solution of the continuous analog of ℓ1 norm minimization. Remarkably, the derived incoherence conditions are satisfied with high probability by random tensor factors uniformly distributed on the sphere, implying global identifiability of random tensor factors.

Original languageEnglish (US)
Pages (from-to)1287-1328
Number of pages42
JournalInformation and Inference
Issue number4
StatePublished - Dec 1 2022


  • atomic norm minimization
  • dual certificate
  • nonconvex
  • super resolution
  • tensor decomposition
  • tensor nuclear norm

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Numerical Analysis
  • Computational Theory and Mathematics
  • Applied Mathematics


Dive into the research topics of 'A super-resolution framework for tensor decomposition'. Together they form a unique fingerprint.

Cite this