Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations

By Min Tao, Xiaoming Yuan. SIAM Journal on Optimization, 2011

483 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cd486929068d8397c080cc8848a0e97ba7789634

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Zaiwen Wen
2. Yi Ma
3. Arvind Ganesh
4. Xiaoming Yuan
5. Bingsheng He
6. Yin Zhang
7. Mingyi He
8. Yuchao Dai

In Computational Mechanics

1. Zhouchen Lin
2. Thierry Bouwmans
3. Wotao Yin
4. Yin Zhang
5. Xuelong Li
6. Zaiwen Wen
7. Xiaoming Yuan
8. Lei Zhang

In Mathematical Physics

1. Bingsheng He
2. Xiaoming Yuan
3. Yin Zhang
4. Liusheng Hou
5. Yinyu Ye
6. Caihua Chen
7. Jieping Ye
8. John Wright

Citations in the corpus

• On the linear convergence of the alternating direction method of multipliers (2012, unknown): “Our analysis is a departure of the conventional analysis of ADMM algorithm which relies on a contraction argument involving a weighted (semi-)norm of ( x r − x ∗ , y r − y ∗ ), see [17–20, 25, 26, 30, 47].”
• Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, methodology): “Moreover, Yuan et al. [438] developed a noise and a blur and noise nuclear-norm-free models SPCP which are detailed in Section 2.2.4.”
• Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation (2011, background): “In previous ADM and LADM approaches [16, 22, 21], the penalty parameter β is fixed.”
• Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization (2012, background): “Here, we mention a few of such applications: image processing [13, 19, 35, 43], compressive sensing [55], SDP [47, 53] and statistics [22, 29, 48].”
• Robust reduced-rank filtering for erratic seismic noise attenuation (2015, background): “…io n su bj ec t t o SE G li ce ns e or c op yr ig ht ; s ee T er m s of U se a t h ttp :// lib ra ry .s eg .o rg / explored for matrix and tensor completion in applied mathematics (Candès et al., 2011; Gandy et al., 2011; Tao and Yuan, 2011) and in seismic data processing (Kreimer et al., 2013).”
• Parallel Multi-Block ADMM with o(1 / k) Convergence (2013, unknown): “See [11, 1, 3, 29, 4, 24, 22, 31, 23] and the references therein for a number of examples.”
• Multidimensional simultaneous random plus erratic noise attenuation and interpolation for seismic data by joint low-rank and sparse inversion (2015, methodology): “We propose to solve the resulting convex optimization problem for each temporal frequency slice with an efficient alternating direction method of multipliers (ADMM) scheme (Wen et al., 2010; Boyd et al., 2011; Tao and Yuan, 2011), which iteratively estimates and recovers the missing entries of the l”
• A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization (2012, methodology): “Thanks to the recent progress in structure from motion and Compressive Sensing, the proposed method can be adapted to handling missing-data case (e.g. Buchanan and Fitzgibbon 2005; Dai et al. 2013; Tao and Yuan 2011), outlier case (e.”
• RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images (2010, background): “Recently, [35] obtained a convergence result for certain three-term alternation ap plied to the noisy principal component pursuit problem (see also [36]).”
• Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization (2014, methodology): “As has been mentioned earlier, the recent algorithm reported in [38] can also handle partial-data model (3), but its cost is relatively high due to the SVD computation, so we omit the comparison with it to save the test time.”
• Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization (2013, methodology): “In the traditional ADMM [46] and linearized ADMM approaches [38], the penalty parameter is fixed.”
• The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent (2014, methodology): “[22, 25]), users have the inclination to imagine that this scheme seems convergent even though they are perplexed by the rigorous proof.”
• Ieee Transactions on Pattern Analysis and Machine Intelligence Laplacian Regularized Low-rank Representation and Its Applications (unknown): “LADMAP FOR SOLVING LAPLACIAN REGULARIZED LRR In recent years, a lot of algorithms have been proposed for solving the optimization problem of recovering a lowrank matrix from the data [26] ,[27],[37],[39] and [42].”
• On Full Jacobian Decomposition of the Augmented Lagrangian Method for Separable Convex Programming (2015, background): “[29, 33]), it was recently shown in [3] that the scheme (1.”