Tensor theta norms and low rank recovery

DOI10.1007/s11075-020-01029-xzbMath1474.13058arXiv1505.05175OpenAlexW3107637484MaRDI QIDQ2048814

Holger Rauhut, Željka Stojanac

Publication date: 24 August 2021

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.05175

zbMATH Keywords

Gröbner basessemidefinite programmingpolynomial idealsconvex relaxationcompressive sensingtheta bodiestensor nuclear normlow rank tensor recovery

Mathematics Subject Classification ID

Semidefinite programming (90C22) Convex programming (90C25) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Convex functions and convex programs in convex geometry (52A41) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Multilinear algebra, tensor calculus (15A69) Sampling theory in information and communication theory (94A20)

Related Items

Low rank tensor recovery via iterative hard thresholding, Algebraic compressed sensing, $N$-Dimensional Tensor Completion for Nuclear Magnetic Resonance Relaxometry, Symmetric Tensor Nuclear Norms, Proximal gradient algorithm for nonconvex low tubal rank tensor recovery, Low-Rank Tensor Recovery using Sequentially Optimal Modal Projections in Iterative Hard Thresholding (SeMPIHT), On polynomial time methods for exact low-rank tensor completion

Uses Software

• UNLocBoX
• SDPNAL+
• PhaseLift

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tensor-Train Decomposition
• On tensor completion via nuclear norm minimization
• Low rank matrix recovery from rank one measurements
• A mathematical introduction to compressive sensing
• Low-rank tensor completion by Riemannian optimization
• A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs
• SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints
• Theta rank, levelness, and matroid minors
• The convex geometry of linear inverse problems
• Low rank tensor recovery via iterative hard thresholding
• An introduction to hierarchical (\(\mathcal H\)-) rank and TT-rank of tensors with examples
• Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal. Translation from the German
• Exact matrix completion via convex optimization
• Completing Any Low-rank Matrix, Provably
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• Proximal Splitting Methods in Signal Processing
• Simultaneously Structured Models With Application to Sparse and Low-Rank Matrices
• Hierarchical Singular Value Decomposition of Tensors
• A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
• Theta Bodies for Polynomial Ideals
• Tensor completion and low-n-rank tensor recovery via convex optimization
• Secant varieties of ℙ² × ℙ ⁿ embedded by 𝒪(1, 2)
• Tensor Spaces and Numerical Tensor Calculus
• Tensor rank is NP-complete
• Tensor Completion in Hierarchical Tensor Representations
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
• On the Shannon capacity of a graph
• Schwartz Spaces, Nuclear Spaces and Tensor Products
• Nuclear norm of higher-order tensors
• Using Algebraic Geometry
• Semidefinite Optimization and Convex Algebraic Geometry
• Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements
• Recovering Low-Rank Matrices From Few Coefficients in Any Basis
• The Power of Convex Relaxation: Near-Optimal Matrix Completion
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• Kronecker Compressive Sensing
• Most Tensor Problems Are NP-Hard
• Compressed sensing