Convex Optimization
One sketch for all: fast algorithms for compressed sensing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Beyond Hirsch Conjecture: Walks on Random Polytopes and Smoothed Complexity of the Simplex Method
SIAM Journal on Computing
Decoding by linear programming
IEEE Transactions on Information Theory
A non-adapted sparse approximation of PDEs with stochastic inputs
Journal of Computational Physics
Iterative reweighted algorithms for matrix rank minimization
The Journal of Machine Learning Research
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Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an l1-minimization problem, and this method is accurate even in the presence of noise. Recently a modified version of this method, reweighted l1-minimization, has been suggested. Although no provable results have yet been attained, empirical studies have suggested the reweighted version outperforms the standard method. Here we analyze the reweighted l1-minimization method in the noisy case, and provide provable results showing an improvement in the error bound over the standard bounds.