Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm

@article{Lu2015NonconvexNL,
  title={Nonconvex Nonsmooth Low Rank Minimization via Iteratively Reweighted Nuclear Norm},
  author={Canyi Lu and Jinhui Tang and Shuicheng Yan and Zhouchen Lin},
  journal={IEEE Transactions on Image Processing},
  year={2015},
  volume={25},
  pages={829-839}
}
The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear norm-based relaxed convex problem usually leads to a suboptimal solution of the original rank minimization problem. In this paper, we propose to use a family of nonconvex surrogates of L0-norm on the singular values of a matrix to approximate the rank function. This leads to a… CONTINUE READING
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