On sparse reconstruction from Fourier and Gaussian measurements

By Mark Rudelson, Roman Vershynin. 2008

901 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/05fd112b31b358135788c669a0f064d4e15f1ba7

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In Computational Mechanics

In Mathematical Physics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

An Improved Estimate in the Restricted Isometry Problem (2014, neutral): “9 from [1] (Maurey’s lemma) logN.”
Sample covariance matrices of heavy-tailed distributions (2016, methodology): “tor |TP(y)| ∈ Rm. Arguments similar in spirit to Lemma 11, and based on Maurey’s empirical method, have been recently employed to verify RIP properties of the Fourier matrices (see, in 10 particular, [23, 6, 12]). Let us note that the dependence on δ of the left-hand side of the bound in Lemma 11 ca”
Exact Recoverability From Dense Corrupted Observations via $\ell _{1}$-Minimization (2011, background): “In this setting [18], each sensor collects information of a signal or object x (cid:63) by simply projecting x (cid:63) onto row vectors a i of a sensing matrix A ∈ R m × n , b i = (cid:104) a i , x (cid:63) (cid:105) .”
Non-asymptotic theory of random matrices: extreme singular values (2010, background): “It was ﬁrst addressed in [17] with a little higher exponent than in (5.4); the exponent 4 was obtained in [64], and it is conjectured that the optimal exponent is 1.”
Living on the edge: phase transitions in convex programs with random data (2013, methodology): “Rudelson & Vershynin [RV08, Sec.”
Imaging via Compressive Sampling (2008, background): “Recovery results exist [2], [ 20 ] that are similar to those using random matrices, but with the additional dependence on a coherence parameter that quantifies how concentrated elements of ψ are in the U domain (and vice versa).”
Precise Undersampling Theorems (2010, background): “We propose the following challenges: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 δ ρ ρ(δ;C,strong) Rudelson & Vershynin Foucart & Lai (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 x 10 −3 δ ρ IHT SP CoSaMP (b) 10 D. Discover an analog o”
Compressed Sensing with Coherent and Redundant Dictionaries (2010, positive): “Since the partial DFT has been proven to satisfy the RIP [16] (see also [37]), it is a fast measurement matrix that can be used in many standard compressed sensing techniques.”
Supplementary Appendix for"Inference on Treatment Effects After Selection Amongst High-Dimensional Controls" (2013, neutral): “Sufficient conditions for the equivalence between population and empirical sparse eigenvalues are given in Rudelson and Zhou (2011) and Rudelson and Ver- shynin (2008).”
Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models (2013, neutral): “[34] Mark Rudelson and Roman Vershynin.”
Kronecker Compressive Sensing (2012, background): “Romberg for pointing us to the remark in [23], to K.”
A Probabilistic and RIPless Theory of Compressed Sensing (2010, methodology): “This can be proved using a theorem of [46] which in turn is a combination of Theorem 6.”
On cross-validated Lasso in high dimensions (2016, neutral): “5) [0, 5] [6, 10] [11, 15] [16, 20] [21, 25] [26, 30] [31, 35] [36, p] (n, p)=(100, 40) 0.”