Basic solvers
1. PCP
- Singular Values Decomposition (SVT)
- Iterative Thresholding (IT)
- Accelerated Proximal Gradient (APG)
- Dual Method (DM)
- Exacted Augmented Lagrangian Method (EALM)
- {nexact Augmented Lagrangian Method (IALM)
- Alternating Direction Method (ADM)
- Symmetric Alternating Direction Method (SADM)
- Non Convex Splitting ADM (NCSADM)
- Douglas-Rachford Splitting Method (DRSM)
- Variant of Douglas-Rachford Splitting Method (VDRSM)
- Proximity Point Algorithm (PPA)
- Proximal Iteratively Reweighted Algorithm (PIRA)
- Alternating Rectified Gradient Method (ARGM)
- Parallel Direction Method of Multipliers (PDMM)
- Generalized Singular Value Thresholding (GSVT)
- Generalized Accelerated Proximal Gradient (GAPG)
- Improved alternating direction method (IADM)
- Optimal Singular Values Shrinkage (OptShrink)
- Iterative Thresholding with Primal-Dual Method (IT-PDM)
- Alternating Minimization (AM)
2. Stable PCP
- Alternating Splitting Augmented Lagrangian method (ASALM)}
- Variational ASALM (VASALM)
- Parallel ASALM (PSALM)
- Non Smooth Augmented Lagrangian Algorithm (NSA)
- First-order Augmented Lagrangian algorithm for Composite norms (FALC)
- Augmented Lagragian method for Conic Convext (ALCC)
- Partially Smooth Proximal Gradient (PSPG)
- Alternating Direction Method - Increasing Penalty (ADMIP)
- Greedy Bilateral Smoothing (GreBsmo)
- {Bilinear Generalized Approximate Message Passing (BiG-AMP)
- Inexact Alternating Minimization - Matrix Manifolds (IAM-MM)
- Customized Proximal Point Algorithm (CPPA)
- multi-block Bregman (BADMM)
- Partially Parallel Splitting - Multiple Block (PPS-MB)
- Local Convex Relaxation (LCR)
- Distributed Douglas-Rachford splitting method (DDRSM)
- Twisted ADMM (TADMM)
Linearized solvers
- Linearized ADM (LADM)
- Linearized ADM with Adaptive Penalty (LADMAP)
- Linearized Symmetric ADM (LSADM)
- Fast Linearized Symmetric ADM (Fast-LSADM)
- Linearized IAD Contraction Methods (LIADCM)
Fast solvers
- Randomized Projection for ALM (RPALM)
- l1-filtering (LF)
- {Block Lanczos with Warm Start
- Exact Fast Robust Principal Component Analysis (EFRPCA)
- Inexact Fast Robust Principal Component Analysis (IFRPCA)
- Matrix Tri-Factorization (MTF)
- Fast Tri-Factorization(FTF)
- PRoximal Iterative SMoothing Algorithm (PRISMA)
- Fast Alterning Minimization (FAM)
- Fast Alternating Direction Method of Multipliers(FADMM)
- Fast Alternating Direction Method with Smoothing Technique (FADM-ST)
- Fast Randomized Singular Value Thresholding (FRSVT)
Online solvers
- Online Alternating Direction Method (OADM)
Non convex solvers
- Difference of Convex (DC)
- Fast Alternating Difference of Convex (FADC)
- Non-convex Alternating Projections(AltProj)
- Iterative Shrinkage-Thresholding/Reweighted Algorithm (ISTRA)
- Fast NonConvex Low-rank (FaNCL)
- Fast RPCA via Gradient Descent (GD)
2D solvers
- Iterative method for Bi-directional Decomposition (IMBD)
Fair Use Policy
As this website gives many information that come from my research, please cite my following survey papers:
T. Bouwmans, A. Sobral, S. Javed, S. Jung, E. Zahzah, "Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset", Computer Science Review, Volume 23, pages 1-71, February 2017. [pdf]
T. Bouwmans, E. Zahzah, “Robust PCA via Principal Component Pursuit: A Review for a Comparative Evaluation in Video Surveillance”, Special Issue on Background Models Challenge, Computer Vision and Image Understanding, CVIU 2014, Volume 122, pages 22–34, May 2014. [pdf]
Note: My publications are available on Academia, Research Gate, Researchr, ORCID and Publication List.