Theta tensor norms and low rank recovery (A06)

• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 442047500

This project investigates an algorithmic approach for the recovery of low rank tensors from incomplete random linear measurements. It is well-known that nuclear norm minimization can provably recover low rank matrices from an optimal number of measurements. Unfortunately,the tensor nuclear norm is NP-hard to compute for tensors of order three or higher. We will therefore consider computable relaxations of the tensor nuclear norm based on theta bodies, a concept from convex algebraic geometry. We aim at proving optimal bounds on the numberof required random measurements for successful recovery.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1481: Sparsity and Singular Structures
• Applicant Institution: Rheinisch-Westfälische Technische Hochschule Aachen
• Project Heads: Professor Dr. Ghislain Fourier; Professor Dr. Holger Rauhut