A Mathematical Introduction to Compressive Sensing

By Simon Foucart, Holger Rauhut. 2013

2,537 citations recorded by the source corpus.

Subfields: Computational Mechanics, Signal Processing

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Citations in the corpus

Inference Under Information Constraints I: Lower Bounds From Chi-Square Contraction (2018, methodology): “where the first inequality is by the decoupling inequality E e T Mθ ≤ E e T Mθ (used in [27] as well) and the second uses sub-Gaussianity once again.”
Compressed Sensing (2014, neutral): “Sin embargo, cuando 0 < q < 1, las funciones `q no son convexas, y el problema asociado (Pq) resulta NP-dif́ıcil [38][Sección 4.”
Stochastic Collocation Algorithms Using l1-Minimization for Bayesian Solution of Inverse Problems (2015, background): “However, this problem is NP-hard in general [15].”
Contextual Bandits with Latent Confounders: An NMF Approach (2016, background): “Statistical RIP property is a randomized variant of the well-known RIP condition [16].”
Online Adaptive Methods, Universality and Acceleration (2018, methodology): “…efﬁcient and fast method, it has found use in numerous applications including: imaging (Chambolle and Pock, 2011), compressed sensing (Foucart and Rauhut, 2013), and deep learning (Sutskever et al., 2013), amongst other. case of stochastic optimization with a smooth expected loss,…”
Convolutional Neural Networks Analyzed via Convolutional Sparse Coding (2016, methodology): “The traditional sparse model has been extensively studied over the past two decades (Elad, 2010; Foucart and Rauhut, 2013).”
Solving inverse problems using data-driven models (2019, neutral): “…at 15:29:08, subject to the Cambridge Core terms of use, available at Finally, in applied harmonic analysis, `p-norms of wavelets have been proposed as regularizers (Daubechies et al. 1991, Mallat 2009, Unser and Blu 2000, Kutyniok and Labate 2012, Eldar and Kutyniok 2012, Foucart and Rauhut 2013).”
Compressed Sensing for Wireless Communications: Useful Tips and Tricks (2015, background): “s presented by Baraniuk [7]. Extended summary can be found in Candes and Wakin [5]. Forucart and Rauhut provided a tutorial of CS with an emphasis on mathematical properties for performance guarantee [8] and similar approach can be found in [9]. Comprehensive treatment on various issues, such as spa”
Hyperbolic Cross Approximation (2016, background): “It turns out that matrices similar to those constructed in [195] and [144] are very important in sparse approximation, namely, in compressed sensing [127], [373].”
Living on the edge: phase transitions in convex programs with random data (2013, background): “See the books [41,43] for background on compressed sensing in general.”
Risk minimization by median-of-means tournaments (2016, methodology): “We refer the reader to the books [22, 16, 40] for more information on sparse recovery and on these procedures.”