Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements

By E.J. Candes, Yaniv Plan. IEEE Transactions on Information Theory, 2011

652 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/25ffa8c55f509241a577a6e6ec85792c66d1f41a

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Citations in the corpus

The Convex Geometry of Linear Inverse Problems (2010, background): “For low-rank matrices, our bound provides sharper constants than those previously derived (for example [15]) and is also applicable over a wider range of matrix ranks and number of measurements than in previous work [64].”
Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-Rank Matrices (2013, background): “In the context of compressed sensing, oracle inequalities have been given in [7], [9], [13], [15] under various settings.”
The non-convex geometry of low-rank matrix optimization (2016, background): “For example, the original convex optimization problems (P0)-(P1) have information-theoretically optimal sampling complexity [15], achieve minimax denoising rate [13] and satisfy tight oracle inequalities [14].”
Geometric median and robust estimation in Banach spaces (2013, background): “In this section, we mainly follow the approach of [23] (Chapter 9) which deals with an important case of sub-Gaussian design (also, see [10,31] for a discussion of related problems), and use results of this work as a basis for our exposition.”
Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview (2018, background): “Fact 1 (RIP for Gaussian matrices [13], [42]): If the entries of Ai are i.”
Dropping Convexity for Faster Semi-definite Optimization (2015, background): “22 A similar but stricter notion is that of restricted isometry property for low rank matrices [20, 54]: Deﬁnition F.1 (Restricted Isometry Property (RIP)) .”
Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators (2012, methodology): “6 Note that [31] contains a typo in Lemma 3.”
Learning Compact Neural Networks with Regularization (2018, neutral): “• Low-rank: T = {W ∈ Bh×p, rank(W ) ≤ r} [7]: logN(T, ε) ≤ (p + h + 1)r log( 9 ε ).”
An Overview of Low-Rank Matrix Recovery From Incomplete Observations (2016, neutral): “This difference is critical for large-scale applications.”
On critical points of quadratic low-rank matrix optimization problems (2020, background): “A typical result is, for example, that specifically scaled random Gaussian matrices give rise to B that satisfy a (k, δk)-RIP with high probability if d ≥ δ−2 k k(m+ n); see [10].”