An ADMM algorithm for a class of total variation regularized estimation problems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 16, Issue PART 1, 2012, Pages 83-88

  Wahlberg, Bo ^a   Boyd, Stephen ^b   Annergren, Mariette ^a   Wang, Yang ^b  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b Stanford University   (United States)

Author keywords

Convex optimization and regularization; Parameter estimation; Signal processing algorithms; Stochastic parameters

Indexed keywords

CONSTRAINED OPTIMIZATION; CONVEX OPTIMIZATION; COST FUNCTIONS; FINANCIAL DATA PROCESSING; LAGRANGE MULTIPLIERS; PARAMETER ESTIMATION; SIGNAL PROCESSING; STOCHASTIC SYSTEMS;

AUGMENTED LAGRANGIAN METHODS; CONVEX OPTIMIZATION PROBLEMS; ESTIMATION PROBLEM; GENERIC OPTIMIZATION; PORTFOLIO OPTIMIZATION; SIGNAL PROCESSING ALGORITHMS; STOCHASTIC PARAMETERS; TRANSACTION COST;

ITERATIVE METHODS;

EID: 84867091929     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20120711-3-BE-2027.00310     Document Type: Conference Paper

References (15)

1. O. Banerjee, L. El Ghaoui, and A. d'Aspremont. Model selection through sparse maximum likelihood estimation for multivariate gaussian or binary data. Journal of Machine Learning Research, 9:485-516, 2008.
2. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein. Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in Machine Learning, 3(1):1-122, 2011.
3. P. L. Combettes and J. C. Pesquet. A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery. Selected Topics in Signal Processing, IEEE Journal of, 1(4):564-574, dec. 2007. ISSN 1932-4553. doi: 10.1109/JSTSP.2007.910264.
4. A. P. Dempster. Covariance selection. Biometrics, 28(1): 157-175, 1972.
5. J. Eckstein and D. P. Bertsekas. On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Mathematical Programming, 55:293-318, 1992.
6. J. Friedman, T. Hastie, and R. Tibshirani. Sparse inverse covariance estimation with the graphical lasso. Biostaüsücs, 9(3):432-441, 2008.
7. M. Grant and S. Boyd. CVX: Matlab software for disciplined convex programming, version 1.21. http://cvxr.com/cvx, April 2011.
8. 1 trend filtering. SIAM Review, 51(2):339-360, 2009.
9. H. Ohlsson, L. Ljung, and S. Boyd. Segmentation of arx-models using sum-of-norms regularization. Automatica, 46:1107-1111, April 2010.
10. L. I. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. Phys. D, 60:259-268, November 1992. ISSN 0167-2789. doi: http://dx.doi.org/10.1016/0167-2789(92)90242-F.
11. Simon Setzer. Operator splittings, bregman methods and frame shrinkage in image processing. International Journal of Computer Vision, 92(3):265-280, 2011.
12. J. Sturm. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11:625-653, 1999. Software available at http://sedumi.ie.lehigh.edu/.
13. R. Tibshirani, M. Saunders, S. Rosset, J. Zhu, and K. Knight. Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67 (Part 1):91-108, 2005.
14. K. Toh, M. Todd, and R. Tütüncü. SDPT3-A Matlab software package for semideflnite programming, version 1.3. Optimization Methods and Software, 11(1):545-581, 1999.
15. 1 mean and variance filtering. Proceedings of the Forty-Fifth Asilomar Conference on Signals, Systems and Computers, 2011. arXiv/1111.5948.