On the Suboptimality of Proximal Gradient Descent for $\ell^{0}$ Sparse Approximation

@article{Yang2017OnTS,
  title={On the Suboptimality of Proximal Gradient Descent for \$\ell^\{0\}\$ Sparse Approximation},
  author={Yingzhen Yang and Jiashi Feng and Nebojsa Jojic and Jianchao Yang and Thomas S. Huang},
  journal={CoRR},
  year={2017},
  volume={abs/1709.01230}
}
We study the proximal gradient descent (PGD) method for l sparse approximation problem as well as its accelerated optimization with randomized algorithms in this paper. We first offer theoretical analysis of PGD showing the bounded gap between the sub-optimal solution by PGD and the globally optimal solution for the l sparse approximation problem under conditions weaker than Restricted Isometry Property widely used in compressive sensing literature. Moreover, we propose randomized algorithms to… CONTINUE READING
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