Compressive Sampling

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Citations in the corpus

GAN Inversion: A Survey (2021, background): “, the signal x∗ ∈ S is sufficiently sparse and measurement matrix A satisfies certain algebraic conditions, such as the restricted isometry property (RSP) [136] or the restricted eigenvalue condition (REC) [137].”
Iteratively reweighted least squares minimization for sparse recovery (2008, background): “We refer the reader to the survey papers [5, 1].”
Greedy approximation (2008, background): “Recent progress (see surveys by Candès (2006) and DeVore (2006)) in compressed sensing has resulted in proving the existence of matrices Φ with k(m,n) n/ log(m/n), which is substantially larger than n1/2.”
Sampling Theorems for Signals From the Union of Finite-Dimensional Linear Subspaces (2009, background): “…a linear map Φ : A (cid:55)→ R N to exist such that it has a Lipschitz constant K F and such that its inverse map It is interesting to note the following argument [35] 5 showing the necessity of the logarithmic dependence on the signal space dimension for signals with bounded l p “norm” ( p ≤ 1 ).”
Supervised Dictionary Learning (2008, background): “It is well known in the statistics, optimization, and compressed sensing communities that the l1 penalty yields a sparse solution, very few non-zero coefficients in α, [3], although there is no explicit analytic link between the value of λ1 and the effective sparsity that this model yields.”
Robust Face Recognition via Sparse Representation (2009, background): “Seeking the sparsest representation therefore automatically discriminates between the various classes present in the training set.”
Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, background): “Examples of solvers include Basis Pursuit (BP) [64][76], Basis Pursuit Denoising (BPDN) [44][51], Orthogonal Matching Pursuit (OMP) [76], Stagewise OMP (StOMP)[84][412], Lattice Matching Pursuit (LaMP) [50], Convex Lattice Matching Pursuit (CoLaMP) [322], Compressive sampling matching pursuit (CoSaM”
On sparse reconstruction from Fourier and Gaussian measurements (2008, unknown): “The survey [2] contains some of the recent results; the compressed sensing webpage [11] documents progress in this area.”
Curvelet-based POCS interpolation of nonuniformly sampled seismic records (2012, background): “Since the innovative theory of compressive sensing (CS) (Candès, 2006; Donoho, 2006), researchers relaxed ‘0 to ‘1 when realizing the presence of the ‘1 term encourages small components of x to become exactly zero, which may result in the same optimal sparsity.”
Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization (2010, background): “Since the -norm is nonconvex, it is often replaced by either the standard -norm or the weighted -norm to make the optimization problem convex [3], [57], [59], [60].”
Constrained sparse Galerkin regression (2016, methodology): “…as the LASSO (Tibshirani 1996) or the sequential thresholded least-squares algorithm used in SINDy, improves the numerical robustness of this identification for noisy overdetermined problems, in contrast to earlier methods (Wang et al. 2011) that used compressed sensing (Candès 2006; Donoho 2006).”
On the Reconstruction of Block-Sparse Signals With an Optimal Number of Measurements (2008, unknown): “In this section we introduce a necessary and sufﬁcient condition on the measurement matrix A so that the optimizations of (1) and (3) are equivalent for all k -block sparse x .”
A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications (2018, background): “The number of measurements required for faithful reconstruction for particular choice of measurement matrix are given in Table 1, where c is a positive constant [6], [7].”
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.”
Learning to invert: Signal recovery via Deep Convolutional Networks (2017, background): “Compressive sensing (CS) [1–3] is a special case of this problem in which the signal has a sparse representation, i.e., there exists an N × N basis matrix Ψ = [ ψ 1 | ψ 2 | . . . | ψ N ] such that x = Ψs and only K ≪ N of the coefﬁcients s are Email: { ali.mousavi, richb } @rice.edu nonzero.”
Fast L1-Minimization Algorithms For Robust Face Recognition (2010, unknown): “In CS theory [2], [3], [4], [5], it has been shown that the minimum (cid:96) 1 -norm solution to an underdetermined system of linear equations is also the sparsest possible solution under quite general conditions.”
1-Bit Matrix Completion (2012, background): “While many of these applications have a relatively long history, recent advances in the closely related ﬁeld of compressed sensing [13, 21, 23] have enabled a burst of progress in the last few years, and we now have a strong base of theoretical results concerning matrix completion [15–17, 25, 30,…”
Trading Accuracy for Sparsity (2009, background): “As mentioned previously, recent work on compressed sensing [Candes and Tao, 2005, Candes, 2006, Donoho, 2006b,a] also provide sufficient conditions for when the minimizer of the `1 relaxed problem is also the solution of the `0 problem.”