Regularization based approaches

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]

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