Fast TV regularization for 2D maximum penalized likelihood estimation

Journal of Computational and Graphical Statistics

Volumn 20, Issue 2, 2011, Pages 479-491

  Mohler, George O ^a   Bertozzi, Andrea L ^a   Goldstein, Thomas A ^a   Osher, Stanley J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Crime; Density estimation; Spatial point process; Split bregman minimization; Total variation

Indexed keywords

EID: 80051610606     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2010.09048     Document Type: Article

References (24)

1. Acar, R., and Vogel, C. R. (1994), "Analysis of Bounded Variation Penalty Methods for Ill-Posed Problems," Inverse Problems, 10, 1217-1229. [485]
2. Chang, T. C., He, L., and Fang, T. (2006), "MR Image Reconstruction From Sparse Radial Samples by Using Bregman Iteration," in Proceedings of the 13th Annual Meeting of ISMRM, Seattle, 696. [482]
3. Davies, P. L., and Kovac, A. (2004), "Densities, Spectral Densities and Modality," The Annals of Statistics, 32, 1093-1136. [480]
4. Eggermont, P. P. B., and LaRiccia, V. N. (2001), Maximum Penalized Likelihood Estimation: Volume I: Density Estimation, New York: Springer. [480]
5. Farrell, G., and Pease, K. (eds.) (2007), Repeat Victimization, New York: Criminal Justice Press. [486]
6. Goldstein, T., and Osher, S. (2009), "The Split Bregman Method for L1 Regularized Problems," SIAM Journal on Imaging Sciences, 2 (2), 323-343. [480-483]
7. Johnson, S. D., Bernasco, W., Bowers, K. J., Elffers, H., Ratcliffe, J., Rengert, G., and Townsley, M. (2007), "Space-Time Patterns of Risk: A Cross National Assessment of Residential Burglary Victimization," Journal of Quantitative Criminology 23, 201-219. [486]
8. Koenker, R., and Mizera, I. (2006), "Density Estimation by Total Variation Regularization," preprint, University of Alberta. [480]
9. Kooperberg, C., and Stone, C. J. (2002), "Logspline Density Estimation With Free Knots," Computational Statistics and Data Analysis, 12, 327-347. [480]
10. Le, T., Chartrand, R., and Asake, T. J. (2007), "A Variational Approach to Reconstructing Images Corrupted by Poisson Noise," Journal of Mathematical Imaging and Vision, 27 (3), 257-263. [480]
11. Mohler, G., Short, M., Brantingham, P., Schoenberg, F., and Tita, G. (2008), "Self-Exciting Point Process Modeling of Crime," in review. [487]
12. Ogata, Y. (1998), "Space-Time Point Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, 50 (2), 379-402. [488]
13. Ogata, Y., and Katsura, K. (1988), "Likelihood Analysis of Spatial Inhomogeneity for Marked Point Patterns," Annals of the Institute of Statistical Mathematics, 40, 20-39. [488]
14. Okabe, A., Boots, B., Sugihara, K., and Chiu, S. (2000), Spatial Tessellations (2nd ed.), Chichester: Wiley. [488]
15. Osher, S., Burger, M., Goldfarb, D., Xu, J., and Yin, W. (2005), "An Iterative Regularization Method for Total Variation-Based Image Restoration," Multiscale Modeling and Simulation, 4, 460-489. [482,483]
16. Peng, R. D., Schoenberg, F. P., and Woods, J. (2005), "A Space-Time Conditional Intensity Model for Evaluating a Wildfire Hazard Index," Journal of the American Statistical Association, 100 (469), 26-35. [488]
17. Rudin, L., Osher, S., and Fatemi, E. (1992), "Nonlinear Total Variation Based Noise Removal Algorithms," Physica D, 60, 259-268. [480,485]
18. Sardy, S., and Tseng, P. (2006), "Density Estimation by Total Variation Penalized Likelihood Driven by the L1 Information Criterion," preprint, University of Washington. [480,485]
19. Scott, D. W. (1992), Multivariate Density Estimation, New York: Wiley. [486]
20. Sheather, S. J., and Jones, M. C. (1991), "A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation," Journal of the Royal Statistical Society, Ser. B, 53, 683-690. [480]
21. Short, M. B., D'Orsogna, M. R., Brantingham, P. J., and Tita, G. E. (2009), "Measuring and Modeling Repeat and Near-Repeat Burglary Effects," Journal of Quantitative Criminology, 25 (3), 325-339. [486]
22. Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman & Hall. [486, 488]
23. Yin, W., Osher, S., Goldfarb, D., and Darbon, J. (2008a), "Bregman Iterative Algorithms for L1-Minimization With Applications to Compressed Sensing," SIAM Journal on Imaging Science, 1, 142-168. [482]
24. Yin, W., Wang, Y., Yang, J., and Zhang, Y. (2008b), "A New Alternating Minimization Algorithm for Total Variation Image Reconstruction," SIAM Journal on Imaging Science, 1 (3), 248-272. [481,482]