Sparsity and incoherence in compressive sampling. Candès, E. & Romberg, J. Inverse Problems, 23(3):969, April, 2007. ![Sparsity and incoherence in compressive sampling [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex We consider the problem of reconstructing a sparse signal from a limited number of linear measurements. Given m randomly selected samples of Ux0, where U is an orthonormal matrix, we show that ℓ1 minimization recovers x0 exactly when the number of measurements exceeds where S is the number of nonzero components in x0 and μ is the largest entry in U properly normalized: . The smaller μ is, the fewer samples needed. The result holds for ‘most’ sparse signals x0 supported on a fixed (but arbitrary) set T. Given T, if the sign of x0 for each nonzero entry on T and the observed values of Ux0 are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about as many samples.
@article{candes_sparsity_2007,
title = {Sparsity and incoherence in compressive sampling},
volume = {23},
issn = {0266-5611},
url = {https://dx.doi.org/10.1088/0266-5611/23/3/008},
doi = {10.1088/0266-5611/23/3/008},
abstract = {We consider the problem of reconstructing a sparse signal from a limited number of linear measurements. Given m randomly selected samples of Ux0, where U is an orthonormal matrix, we show that ℓ1 minimization recovers x0 exactly when the number of measurements exceeds where S is the number of nonzero components in x0 and μ is the largest entry in U properly normalized: . The smaller μ is, the fewer samples needed. The result holds for ‘most’ sparse signals x0 supported on a fixed (but arbitrary) set T. Given T, if the sign of x0 for each nonzero entry on T and the observed values of Ux0 are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about as many samples.},
language = {en},
number = {3},
urldate = {2024-03-19},
journal = {Inverse Problems},
author = {Candès, Emmanuel and Romberg, Justin},
month = apr,
year = {2007},
keywords = {/unread},
pages = {969},
}
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