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This paper considers the task of recovering the support of a sparse, high-dimensional vector from a small number of measurements. The procedure proposed here, which we call the Sign-Sketch procedure, is shown to be a robust recovery method in settings where the measurements are corrupted by various forms of uncertainty, including additive Gaussian noise and (possibly unbounded) outliers, and even...
The problem of consistently estimating the sparsity pattern of a vector beta* isin Rp based on observations contaminated by noise arises in various contexts, including signal denoising, sparse approximation, compressed sensing, and model selection. We analyze the behavior of l1-constrained quadratic programming (QP), also referred to as the Lasso, for recovering the sparsity pattern. Our main result...
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