Handbook on "Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing"



T. Bouwmans,  N. Aybat, E. Zahzah

  • Tentative publication date:  May 30, 2016
  • Preface introducing the field of robust decomposition in low rank and sparse matrices, and the different chapters:

This handbook solicited contributions in the field of robust decomposition in low rank and sparse matrices. By incorporating both existing and new ideas, this handbook gives a complete overview of the concepts, theories, algorithms, and applications related to robust decomposition in low rank and sparse matrices. Moreover, an accompanying website is provided. This website contains the list of chapters, their abstract and links to the demos. It allows the reader to have a quick access to the main resources, datasets and codes in the field. Finally, with this handbook, we aim to bring a one-stop solution, i.e., access to a number of different decomposition, solvers, implementations and benchmarking techniques in a single volume. The handbook consists of five parts.

This website contains the list of chapters, their abstract and links to the demos. It allows the reader to have a quick access to the main resources, datasets and codes in the field.



  • About the editors: T. Bouwmans, N. Aybat, E. Zahzah (more details)
  • List of contributors:  The contributors are representative researchers in the field. (more details)
  • Dedication: The dedication is written by Emmanuel Candès. (more details)
  • Contents (5 Parts, 21 Chapters)

Part I. Robust Principal Component Analysis


Chapter 1 -  Robust Principal Component Analysis via Decomposition into Low-rank and Sparse Matrices: An overview

T. Bouwmans (Lab MIA, Univ. La Rochelle, France), E. Zahzah (Lab L3i, Univ. La Rochelle, France)

Chapter 2 - Algorithms Stable PCA

N. Aybat (Pennsylvania State University, USA)

Chapter 3 - Dual Smoothing and Value Function Techniques for Variational Matrix Decomposition

A. Aravkin (IBM TJ Watson Research Center, USA), S. Becker (University of Colorado,USA)


Chapter 4 -
Robust Principal Component Analysis based on Low-Rank and Block-Sparse Matrix Decomposition

Q. Li (Colorado School, USA), G. Tang (Colorado School, USA), A. Nehorai (Washington University, USA)

Chapter 5 - Robust PCA by controlling sparsity in model residuals

G. Mateos (Univ. of Rochester, USA), G. Giannakis (Univ. of Minnesota, USA)

Part II. Robust Matrix Factorization/Completion


Chapter 6 - Unifying Nuclear Norm and Bilinear Factorization for Low Rank Matrix Decomposition

R. Cabral (Carnegie Mellon University,USA), F. De la Torre (Carnegie Mellon University,USA), J. Costeira (Instituto Superior Técnico, Portugal), A. Bernardino (Instituto Superior Técnico, Portugal)

Chapter 7 - Robust Non-negative Matrix Factorization under Separability Assumption

A. Kumar (IBM T.J. Watson Research Center, USA),  V. Sindhwani (Google Research, NY, USA)

Chapter 8 - Robust Matrix Completion through Nonconvex Approaches and Efficient Algorithms

Y. Yang (Belgium) , Y. Feng (Belgium), J. Suykens (Belgium)

Chapter 9 - Factorized Robust Matrix Completion

H. Mansour (MERL, USA),  D. Tian (MERL, USA), A. Vetro (MERL, USA)


Part III. Robust Online Subspace Estimation, Learning and Tracking


Chapter 10Online Robust Principal Components Analysis

N. Vaswani (Iowa State University, USA), C. Qiu (Iowa State University, USA), B. Lois (Iowa State University, USA), H. Guo  (Iowa State University, USA), J. Zhan (Iowa State University, USA)

Chapter 11 - Incremental Methods for Robust Local Subspace Estimation

B. Wohlberg (Los Alamos National Laboratory, USA), P. Rodriguez (Pontificia Universidad Catolica del Peru, Peru)

Chapter 12 - Robust Orthonormal Subspace Learning (ROSL) for Efficient Low-rank Recovery

X. Shu (Qualcomm, San Diego, USA), F. Porikli (Australian National University/NICTA, Australia), N. Ahuja (University of Illinois, Urbana-Champaign, USA)

Chapter 13 -  A Unified View of Nonconvex Heuristic Approach for Low-rank and Sparse Structure Learning

Y. Deng (Tsinghua University, China), F. Bao (Tsinghua University, China), Q. Dai (Tsinghua University, China)


Part IV.  Applications in Image and Video Processing


Chapter 14 - A Variational Approach for Sparse Component Estimation and Low-Rank Matrix Recovery

Z. Chen (Northwestern University, Illinois, USA), R. Molina (Universidad de Granada, Spain), A. Katsaggelos (Northwestern University, USA)

Chapter 15 - Recovering Low-Rank and Sparse Matrices with Missing and Grossly Corrupted Observations

F. Shang (University of Hong Kong), Y. Liu (University of Hong Kong), J. Cheng (University of Hong Kong), H. Cheng (University of Hong Kong) 

Chapter 16 - Applications of Low Rank and Sparse Matrix Decompositions in Hyperspectral Video Processing

J. Chang (California State University, Long Beach, USA), T. Gerhart (Western Digital Corporation, USA)

Chapter 17 - Low-rank plus sparse dynamic MRI: Accelerated data acquisition, separation of background and dynamic components and self-learning of motion fields

R. Otazo (New York University, USA), E. Candes (University of Stanford), D. Sodickson (New York University, USA)


Part V. Applications in Background/Foreground Separation for Video Surveillance


Chapter 18 - LRSLibrary: Low-Rank and Sparse tools for Background Modeling and Subtraction in Videos

A. Sobral (Lab L3i, Univ. La Rochelle, France), T. Bouwmans (Lab MIA, Univ. La Rochelle, France), E. Zahzah (Lab L3i, Univ. La Rochelle, France)

Chapter 19 - Dynamic Mode Decomposition for Robust PCA with Applications to Foreground/Background Subtraction in Video Streams

J. Grosek (University of Washington, USA), X. Fu (University of Washington, USA), S. Brunton (University of Washington, USA), J. Nathan Kutz (Air Force Research Laboratories, USA)

Chapter 20 - Stochastic RPCA for Background/Foreground Separation

S. Javed (Kyungpook National University, Korea), S. Oh (Kyungpook National University, Korea), T. Bouwmans (Lab MIA, Univ. La Rochelle, France), S. Jung (Kyungpook National University, Korea)

Chapter 21 - Bayesian Sparse Estimation for Background/Foreground Separation

S. Nakajima (Technische Universität Berlin), Masashi Sugiyama (University of Tokyo), S. Derin Babacan (Google Inc.)