A Unified View of Robust Decomposition in Sparse + Additive Matrices for Computer Vision
Sparse decompositions are similar to low-rank decompositions except that the first matrix is considered to be sparse instead of low-rank. Sparse decompositions are achieved in the different following problem formulations: Sparse dictionary learning, sparse linear approximation and compressive sensing.
Robust Decomposition in Sparse + Additive Matrices
All the decompositions in these different problem formulations of robust subspace learning/tracking can be considered in a unified view that we called Decomposition into Sparse plus Additive Matrices (DSAM). Thus, all the decompositions can be written in a general formulation as follows:
- The first matrix M1 is a low-rank matrix S.
- The second matrix M2 is an unconstrained (residual) matrix E.
Key Characteristics
Applications to Statistical Modeling and Computer Vision
The different robust problem formulations based on the decomposition into sparse plus additive matrices are fundamental in several applications . Indeed, as this decomposition is nonparametric and does not make many assumptions, it is widely applicable to a large scale of problems ranging from:
- Image processing
- Video processing (background and foreground separation)
Author: Thierry BOUWMANS, Associate Professor, Lab. MIA, Univ. Rochelle, France.
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, November 2016. [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]