Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit

By Joel A. Tropp, Anna C. Gilbert. 2007

7,091 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Signal Processing

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Citations in the corpus

Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, methodology): “This formulation is closely related to the compressive sensing framework, which allows for the sparse vector ξ to be determined from relatively few incoherent random measurements [15, 16, 17, 18, 19, 20].”
Iterative Hard Thresholding for Compressed Sensing (2008, methodology): “A by now traditional approach is Orthogonal Matching Pursuit [9], which was analysed as a reconstruction algorithm for compressed sensing in [ 10 ].”
Solving inverse problems using data-driven models (2019, background): “Other examples are matching pursuit (MP) (Mallat and Zhang 1993), orthogonal matching pursuit (OMP) (Tropp and Gilbert 2007) and variants thereof such as StOMP (Donoho, Tsaig, Drori and Starck 2012), ROMP (Needell and Vershynin 2009) and CoSamp (Needell and Tropp 2009).”
Hyperspectral and Multispectral Image Fusion Based on a Sparse Representation (2014, methodology): “(14) 11 Algorithm 1: Fusion of HS and MS based on a sparse representation Input: YH, YM, SNRH, SNRM, m̃λ (HS subspace dimension),R, B, S, K % Propose a rough estimation Ũ of U 1 ComputeŨ , µ̂U|YM following the method in [17] (see Appendix); 2 for i = 1 to m̃λ do % Online dictionary learning 3 D̄i ”
Channel estimation for OFDM systems (2017, methodology): “to [14, 18], there are algorithms that can solve BP in time O(IK).”
Cross-View Action Recognition via Transferable Dictionary Learning (2016, background): “The interest in action recognition is motivated by many real-world applications, such as creating large video archives, human computer interaction, and video surveillance.”
Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse (2008, methodology): “Perhaps surprisingly, optimists can cite theoretical work supporting this notion; work by Tropp et al. [52, 54 ] and Donoho et al. [19] has shown that Omp can, in certain circumstances, succeed at finding the sparsest solution.”
Compressive Sensing by Random Convolution (2009, methodology): “The ensemble is generated by drawing each element independently from a subgaussian [6, 10 , 15, 24] distribution.”
Beamforming for Millimeter Wave Communications: An Inclusive Survey (2016, methodology): “From an implementation perspective, a low-complexity reconstruction algorithm for joint RF-baseband precoder based on simultaneous OMP that enables highly parallel hardware architecture is presented in [184].”
Fast global convergence rates of gradient methods for high-dimensional statistical recovery (2010, background): “Such a condition corresponds to a variant of the restricted eigenvalue (RE) conditions that have been studied in the literature [7, 42].”
RF Sensor Networks for Device-Free Localization: Measurements, Models, and Algorithms (2010, methodology): “Secondly, the image can be obtained using the LASSO technique [59], and thirdly, using orthogonal matching pursuit (OMP) [60] [15].”
Bayesian sparse representation for hyperspectral image super resolution (2015, methodology): “Orthogonal Matching Pursuit [26] and Basis Pursuit [12], but their performance is inferior when used with the Bayesian dictionaries learned using the Beta process.”
An Architecture for Compressive Imaging (2006, methodology): “Examples include the iterative Orthogonal Matching Pursuit (OMP) [ 8 ], matching pursuit (MP), and tree matching pursuit (TMP) algorithms.”
Harmless interpolation of noisy data in regression (2019, background): “The ﬁrst theoretical guarantees on OMP were proved for noiseless recovery, when OMP is run to completion in the absence of noise [17].”