Compressed sensing

By David L. Donoho. IEEE Transactions on Information Theory, 2006

1,410 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/9fb8c76e6b17f3fdbd0c8f293ce8da4b79f4ffeb

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In Applied Mathematics

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Sparsity and incoherence in compressive sampling (2006, background): “We also note that since [4], several papers have appeared on using `1 minimization to recover sparse signals from a limited number of measurements [5, 7, 9].”
Linearized Bregman iterations for compressed sensing (2009, background): “The interested reader should consult, for example, [2, 8, 9, 10, 11, 12, 19, 21, 22, 23, 24, 29, 30, 31, 33, 34] for details.”
Message-passing algorithms for compressed sensing (2009, background): “Extensive numerical and Monte Carlo work reported here shows that AMP, defined by eqns [1], [2] achieves a sparsity-undersampling tradeoff matching the theoretical tradeoff which has been proved for LP-based reconstruction.”
Learning Deep Architectures for AI (2007, background): “Sparsity has become a concept of great interest recently, not only in machine learning but also in statistics and signal processing, in particular with the work on compressed sensing [30, 47], but it was introduced earlier in computational neuroscience in the context of sparse coding in”
Compressed Least-Squares Regression (2009, neutral): “the Basis Pursuit [10]), and assuming that the target function admits a sparse decomposition, the field of Compressed Sensing [9, 22] provides sufficient conditions for recovering the exact solution.”
On a generalization of the iterative soft-thresholding algorithm for the case of non-separable penalty (2011, methodology): “iest (not necessarily the most eﬃcient) is the iterative soft-thresholding algorithm [1] (see also section 3). As ℓ 1-norm penalties promote sparsity, such algorithms are used in ‘compressed sensing’ [2] for ﬁnding a sparse solution (up to noise level) of a large-scale under-determined linear system”
Compressed sensing and best k-term approximation (2008, background): “The ideas have their origins in certain abstract results from functional analysis and approximation theory by Kashin [23] but were recently brought into the forefront by the work of Candès, Romberg and Tao [7, 5, 6] and Donoho [9] who constructed concrete algorithms and showed their promise in appli”
Error correction via linear programming (2005, positive): “With the subsequent development of fast interior point methods in Linear Programming, (P1) turned into an effectively solvable problem, and was put forward more recently by Donoho and his collaborators, triggering massive experimental and theoretical work [5, 7, 8, 10, 14, 15, 17–21, 23, 27, 33, 45–”
The Dantzig selector: Statistical estimation when P is much larger than n (2005, background): “quire against incoherent waveforms as discussed in the previous sections. Then one would eﬀectively be able to make up a digital image with far fewer sensors than what is usually considered necessary [14, 19]. 3. Sensor networks. There are promising applications in sensor networks where taking rando”
Non-parametric seismic data recovery with curvelet frames (2008, neutral): “This incapability explains why wavelets do not improve the compression rate for data with wavefronts as much as recently developed directional curvelet frames do (Candès and Donoho, 2000a, 2004; Candès and Donoho, 2005a,b).”
A high-bias, low-variance introduction to Machine Learning for physicists (2018, neutral): “Much of this research has focused on understanding high-dimensional linear regression and compressed sensing (Donoho, 2006) (see (Advani et al., 2013; Zdeborová and Krzakala, 2016) for accessible reviews for physicists).”
Random Sampling of Sparse Trigonometric Polynomials (2005, background): “In [10, 11] Donoho and Tsaig introduce the terminology “compressed sensing” for this range of problems and in [12, 13] probabilistic results concerning Basis Pursuit are discussed.”
Compressive Radar Imaging (2007, methodology): “It can be shown that many random measurement matrices are universal in the sense that they are incoherent with any fixed basis Ψ (spikes, sinusoids, wavelets, Gabor functions, curvelets, and so on) with high probability [2], [3], [5].”
An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression (2007, background): “2001), signal recovery from incomplete measurements (Candès et al., 2006, 2005; Donoho, 2006), and wavelet thresholding (Donoho et al.”