Abstract
For the problem of sparse recovery, it is widely accepted that nonconvex minimizations are better than ℓ1 penalty in enhancing the sparsity of solution. However, to date, the theory verifying that nonconvex penalties outperform (or are at least as good as) ℓ1 minimization in exact, uniform recovery has mostly been limited to separable cases. In this paper, we establish general recovery guarantees through null space conditions for nonconvex, non-separable regularizations, which are slightly less demanding than the standard null space property for ℓ1 minimization.
Original language | English |
---|---|
Article number | 100011 |
Journal | Results in Applied Mathematics |
Volume | 3 |
DOIs | |
State | Published - Oct 2019 |
Funding
This material is based upon work supported in part by: the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under contracts and awards ERKJ314, ERKJ331, ERKJ345; and Scientific Discovery through Advanced Computing (SciDAC) program through the FASTMath Institute under Contract No. DE-AC02-05CH11231; and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory, which is operated by UT-Battelle, LLC., for the U.S. Department of Energy under contract DE-AC05-00OR22725. This material is based upon work supported in part by: the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under contracts and awards ERKJ314 , ERKJ331 , ERKJ345 ; and Scientific Discovery through Advanced Computing (SciDAC) program through the FASTMath Institute under Contract No. DE-AC02-05CH11231 ; and by the Laboratory Directed Research and Development program at the Oak Ridge National Laboratory , which is operated by UT-Battelle, LLC. , for the U.S. Department of Energy under contract DE-AC05-00OR22725 .
Keywords
- 90C26
- 94A12
- 94A15
- Majorization theory
- Nonconvex optimization
- Null space property
- Sparse recovery