A Fast Algorithm for Sparse Reconstruction Based on Shrinkage, Subspace Optimization, and Continuation

@article{Wen2010AFA,
  title={A Fast Algorithm for Sparse Reconstruction Based on Shrinkage, Subspace Optimization, and Continuation},
  author={Zaiwen Wen and Wotao Yin and Donald Goldfarb and Yin Zhang},
  journal={SIAM J. Scientific Computing},
  year={2010},
  volume={32},
  pages={1832-1857}
}
We propose a fast algorithm for solving the $\ell_1$-regularized minimization problem $\min_{x\in\mathbb{R}^n}\mu\|x\|_1+\|Ax-b\|^2_2$ for recovering sparse solutions to an undetermined system of linear equations $Ax=b$. The algorithm is divided into two stages that are performed repeatedly. In the first stage a first-order iterative “shrinkage” method yields an estimate of the subset of components of $x$ likely to be nonzero in an optimal solution. Restricting the decision variables $x$ to… CONTINUE READING

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