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Iteratively reweighted least squares minimization for sparse recovery
| Venue: | Comm. Pure Appl. Math |
| Citations: | 156 - 5 self |
BibTeX
@ARTICLE{Daubechies_iterativelyreweighted,
author = {Ingrid Daubechies and Ronald Devore and Massimo Fornasier and C. Sinan Güntürk},
title = {Iteratively reweighted least squares minimization for sparse recovery},
journal = {Comm. Pure Appl. Math},
year = {}
}
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Abstract
Under certain conditions (known as the Restricted Isometry Property or RIP) on the m ×Nmatrix Φ (where m < N), vectors x ∈ RN that are sparse (i.e. have most of their entries equal to zero) can be recovered exactly from y: = Φx even though Φ−1 (y) is typically an (N − m)dimensional hyperplane; in addition x is then equal to the element in Φ−1 (y) of minimal ℓ1-norm. This minimal element can be identified via linear programming algorithms. We study an alternative method of determining x, as the limit of an Iteratively Re-weighted Least Squares (IRLS) algorithm. The main step of this IRLS finds, for a given weight vector w, the element in Φ−1 (y) with smallest ℓ2(w)-norm. If x (n) is the solution at iteration step n, then the new weight w (n) is defined by w (n) i:=
