Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting
نویسندگان
چکیده
منابع مشابه
Sharp thresholds for high-dimensional and noisy recovery of sparsity
The problem of consistently estimating the sparsity pattern of a vector β∗ ∈ R based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in graphical models, sparse approximation, and signal denoising. We analyze the behavior of l1-constrained quadratic programming (QP), also referred to as the Lasso, for recovering th...
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Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on the scaling law of the number of measurements for successful support recovery have been derived where the main focus is on random Gaussian measurement matri...
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The problem of consistently estimating the sparsity pattern of a vector β ∈ R 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 is...
متن کاملSharp thresholds for high-dimensional and noisy recovery of sparsity using l1-constrained quadratic programming
The problem of consistently estimating the sparsity pattern of a vector β∗ ∈ R 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 i...
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The problem of consistently estimating the sparsity pattern of a vector 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 -constrained quadratic programming (QP), also referred to as the Lasso, for recovering the sparsity pattern. Our main result is to esta...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2009
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2009.2032816