Iteratively re-weighted least squares minimization for sparse recovery
Preprint
Abstract
We analyze an Iteratively Re-weighted Least Squares (IRLS) algorithm for promoting l1-minimization in sparse and compressible vector recovery. We prove its convergence and we estimate its local rate. We show how the algorithm can be modified in order to promote lt-minimization for t<1, and how this modification produces superlinear rates of convergence.Keywords
All Related Versions
This publication has 25 references indexed in Scilit:
- Enhancing Sparsity by Reweighted ℓ 1 MinimizationJournal of Fourier Analysis and Applications, 2008
- Compressed sensing and best 𝑘-term approximationJournal of the American Mathematical Society, 2008
- Restricted isometry properties and nonconvex compressive sensingInverse Problems, 2008
- A Simple Proof of the Restricted Isometry Property for Random MatricesConstructive Approximation, 2008
- On sparse reconstruction from Fourier and Gaussian measurementsCommunications on Pure and Applied Mathematics, 2007
- Highly sparse representations from dictionaries are unique and independent of the sparseness measureApplied and Computational Harmonic Analysis, 2007
- Stable signal recovery from incomplete and inaccurate measurementsCommunications on Pure and Applied Mathematics, 2006
- High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to DimensionDiscrete & Computational Geometry, 2005
- Sparse nonnegative solution of underdetermined linear equations by linear programmingProceedings of the National Academy of Sciences, 2005
- Image recovery via total variation minimization and related problemsNumerische Mathematik, 1997