Objective

The aim of this web site is to provide resources such as references (1205 papers), codes (33 codes) and links to demonstration websites (29 websites)  for the research on decomposition into low-rank plus additive matrices by grouping all related researches and particularly recent advances in this field.  For this, it  is organized in the following sections:

1. Different Problem Formulations (710 papers)

Robust Principal Component Analysis (RPCA) (569 papers), Robust Non-negative Matrix Factorization (RNMF) (6 papers),

Robust Subspace Recovery (RSR) (9 papers), Robust Subspace Tracking (RST) (29 papers), 

Robust Subspace Change-Point Detection (RSCD) (2 papers), Robust Matrix Completion (RMC) (30  papers), 

Robust Low Rank Minimization (LRM) (63 papers), Robust Graph Learning (RGL) (1 paper),

Robust Graphical Lasso (1 paper)

2. Minimization Problem

3. Solvers

Regularization based approaches, Statistical inference based approaches

4. Norms

5. Surveys (25 papers)

6. Applications (472)

6.1 Applications in Statistics (7 papers)

Statistical Modeling (3 papers), Classification Modeling (1 paper), Financial Engineering (3 papers)

6.2. Applications in Machine Learning (1 paper)

Adversarial Attacks (1 paper)

6.3 Applications in Signal Processing (178 papers)

Signal Communication (11 papers), Seismology (10 papers), Audio Signal Processing (49 papers), Radar (99 papers), Direction-of-Arrival Tracking (4 papers), Cognitive Radio (2 papers), Harmonic Recovery (1 paper), Spectrum Denoising (1 paper)

6.4 Applications in Computer Vision (247 papers)

      6.4.1 Image Processing (74 papers)

Image Analysis (1 paper), Image Decomposition (4 papers), Image Classification (1 paper), lmage Composition (1 paper), Image Colorization (1 paper), Image Restoration and Denoising (12 papers),  Image Mosaicking (1 paper), Image Alignment and Rectification (10 papers), Image Fusion (3 papers), Image Search (1 paper), Image Retrieval (1 paper), Texture (4 papers),  Face Alignement/Clustering/Recognition (10 papers), Multi-focus Image (5 papers) ,Multi-spectral Image (2 papers), Hyperspectral Image Processing (11 papers), Saliency Detection (5 papers), Groupwise Image Registration (1 paper)

     6.4.2 Video Processing (119 papers)

Change Detection (1 paper), Crowd Visual Localization (1 paper), Background Initialization (4 papers),

Background/Foreground Separation for Static RGB Cameras (5 papers),

Background/Foreground Separation for Static IR Cameras (2 papers), 

Background/Foreground Separation for Static Multi-spectral Cameras (2 papers),

Background/Foreground Separation for Camera Traps (3 papers),

Background/Foreground Separation for Moving Cameras (6 papers), 

Small Target Detection in Infrared Cameras (32 papers),

Hyperspectral Video Processing (33 papers),

Moving Target Detection (1 paper), Motion Saliency Detection (1 paper),  Motion Estimation (1 paper), Tracking (7 papers),Video Coding (4 papers), Video Denoising (5 papers), Video Object Segmentation (3 papers), Video Restoration (1 paper),  Video Summarization (1 paper), Key Frame Extraction (1 paper),  Action Recognition (1 paper), Event Detection (2 papers), Video UHD Super Resolution Video (1 paper) 

     6.4.3 3D Computer Vision (17 papers)

Structure from Motion (9 papers), Motion Recovery (1 paper), 3D Reconstruction (5 papers),  3D Human Pose Recovery (1 paper), Background/Foreground Separation for 3D (1 paper)

6.5 Applications in Computer Graphics (4 papers)

6.6 Applications in Computer Science (13 papers)

Networks (13 papers)

6.7 Applications in Astronomy (4 papers)

Ionospheric Ionogram Denoising (1 paper), Auroral Substorm Detection (1 paper), Exoplanet Detection (2 papers)

6.8 Applications in Industrial Process (37 papers)

Electricity (13 papers), Chemometrics (3 papers), Defect Detection (16 papers), Damage Detection (5 papers), Fault Detection (1 paper)

6.9 Applications in Physics (7 papers)

6.10 Application in Other Applications (13 papers)

Ecology (1 paper), Electronic Support Receivers (1 paper), Sensors Placement (1 paper), Feature Selection (2 papers), Recognition (5 papers), Database Reconstruction (1 paper), Storyline From a Narrative (2 papers)

7. Available Implementations (33 implementations)

Robust Principal Component Analysis (19 implementations), Robust Non-negative Matrix Factorization (2 implementations), Robust Matrix Completion (2 implementations), Robust Subspace Recovery (1 implementation), Robust Subspace Tracking (5 implementations), Robust Low Rank Minimization (4 implementations)

Note: The number in parenthesis gives the total amount of papers or links for the related categories.