Bregman Iterative Algorithms for \ell1-Minimization with Applications to Compressed Sensing

@article{Yin2008BregmanIA,
  title={Bregman Iterative Algorithms for \ell1-Minimization with Applications to Compressed Sensing},
  author={Wotao Yin and Stanley Osher and Donald Goldfarb and J{\'e}r{\^o}me Darbon},
  journal={SIAM J. Imaging Sciences},
  year={2008},
  volume={1},
  pages={143-168}
}
We propose simple and extremely efficient methods for solving the Basis Pursuit problem min{‖u‖1 : Au = f, u ∈ R}, which is used in compressed sensing. Our methods are based on Bregman iterative regularization and they give a very accurate solution after solving only a very small number of instances of the unconstrained problem min u∈Rn μ‖u‖1 + 1 2 ‖Au− f‖2, for given matrix A and vector fk. We show analytically that this iterative approach yields exact solutions in a finite number of steps… CONTINUE READING
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