Optimal Injectivity Conditions for Bilinear Inverse Problems with Applications to Identifiability of Deconvolution Problems

DOI10.1137/16M1067469zbMath1365.15021arXiv1603.07316OpenAlexW2963507583WikidataQ122897659 ScholiaQ122897659MaRDI QIDQ5347292

Felix Krahmer, Michael Kech

Publication date: 23 May 2017

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.07316

zbMATH Keywords

injectivityuniquenessdeconvolutionidentifiabilitybilinear inverse problems

Mathematics Subject Classification ID

Questions of classical algebraic geometry (51N35) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Inverse problems in linear algebra (15A29) Projective techniques in algebraic geometry (14N05) Quadratic and bilinear forms, inner products (15A63)

Related Items (14)

Efficient Identification of Butterfly Sparse Matrix Factorizations ⋮ Almost everywhere generalized phase retrieval ⋮ Almost everywhere injectivity conditions for the matrix recovery problem ⋮ Convex and Nonconvex Optimization Are Both Minimax-Optimal for Noisy Blind Deconvolution Under Random Designs ⋮ Sparse blind deconvolution and demixing through \(\ell_{1,2}\)-minimization ⋮ Riemannian thresholding methods for row-sparse and low-rank matrix recovery ⋮ Exact Recovery of Multichannel Sparse Blind Deconvolution via Gradient Descent ⋮ Maximum Likelihood Estimation of Regularization Parameters in High-Dimensional Inverse Problems: An Empirical Bayesian Approach. Part II: Theoretical Analysis ⋮ Sparse power factorization: balancing peakiness and sample complexity ⋮ Self-Calibration and Bilinear Inverse Problems via Linear Least Squares ⋮ Spectral Methods for Passive Imaging: Nonasymptotic Performance and Robustness ⋮ Proof methods for robust low-rank matrix recovery ⋮ Information theory and recovery algorithms for data fusion in Earth observation ⋮ Geometry and Symmetry in Short-and-Sparse Deconvolution

Uses Software

• PhaseLift

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