Sparse Recovery via Partial Regularization: Models, Theory and Algorithms

@article{Lu2015SparseRV,
  title={Sparse Recovery via Partial Regularization: Models, Theory and Algorithms},
  author={Zhaosong Lu and Xiaorui Li},
  journal={ArXiv},
  year={2015},
  volume={abs/1511.07293}
}
In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class of models with partial regularizers for recovering a sparse solution of a linear system. We show that every local minimizer of these models is sufficiently sparse or the magnitude of all its nonzero entries is above a uniform constant depending only on the… CONTINUE READING
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