Null Space Property

Dictionary-Sparse Recovery From Heavy-Tailed Measurements

The recovery of signals that are sparse not in a given basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard …

Iteratively Reweighted Least Squares for $\ell_1$-minimization with Global Linear Convergence Rate

Iteratively Reweighted Least Squares (IRLS), whose history goes back more than 80 years, represents an important family of algorithms for non-smooth optimization as it is able to optimize these problems by solving a sequence of linear systems. In …

Harmonic Mean Iteratively Reweighted Least Squares for Low-Rank Matrix Recovery

We propose a new iteratively reweighted least squares (IRLS) algorithm for the recovery of a matrix $X \in \mathbb{C}^{d_1 \times d_2}$ of rank $r \ll \min(d_1,d_2)$ from incomplete linear observations, solv- ing a sequence of low complexity linear …