The Bregman Iterative Procedure
- Visit the page for Linearized Bregman.
W. Yin and S. Osher. "Error Forgetting of Bregman Iteration." Submitted to Journal of Scientific Computing, Special Issue. Rice CAAM Technical Report TR12-03 [pdf] [code]
Explain why solving Bregman subproblems at low accuracies (1e-6) gives a Bregman solution at near the machine precision (1e-15).
- W. Yin, S. Osher, J. Darbon, and D. Goldfarb. "Bregman Iterative Algorithms for Compressed Sensing and Related Problems." SIAM Journal on Imaging Sciences, 1(1):143-168, 2008. [pdf]
- S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin. "An iterative regularization method for total variation-based image restoration." SIAM Journal on Multiscale Modeling and Simulation, 4(2):460-489, 2005. [pdf]
Do not confuse this with the linearized Bregman method!
- Matlab demo of error forgetting [zip]
Two different usages of Bregman iteration:
- To improve the regularization quality of nonsmooth regularizers such as L1, total variations, and their variants; see [slides 6-10] for a demo.
- To give fast, accurate iterations for constrained L1-like minimization. It enjoys error forgetting and cancellation properties; see [slides 25-27] and the Matlab demo below.