Extensions of compressed sensing

By Yaakov Tsaig, David L. Donoho. Signal Processing, 2006

741 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/1a4b96e71b72af9d140b4f7a4f0fb027a592d4d7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Richard Baraniuk
2. E.J. Candes
3. Marco F. Duarte
4. David L. Donoho
5. Michael Elad
6. Lei Zhang
7. Yonina C. Eldar
8. Holger Rauhut

In Computer Vision and Pattern Recognition

1. Lei Zhang
2. Michael Elad
3. Richard Baraniuk
4. Luc Van Gool
5. David L. Donoho
6. Dacheng Tao
7. E.J. Candes
8. Felix J. Herrmann

In Radiology, Nuclear Medicine and Imaging

1. David L. Donoho
2. Michael Elad
3. Richard Baraniuk
4. E.J. Candes
5. Michael Lustig
6. Stanley J. Osher
7. Felix J. Herrmann
8. Lawrence Carin

Citations in the corpus

• Distributed Compressive Sensing (2009, methodology): “ThetypicalperformanceofBasisPursuit-basedCSsignalrecoveryisillustratedinFigure2.”
• Recovering Sparse Signals With a Certain Family of Nonconvex Penalties and DC Programming (2009, neutral): “In this framework, the noise free situation is handled by considering the linear constraint y = Xβ rather than the inequality constraint and have led to numerous papers, especially those related to compressed sensing [7], [16].”
• Bayesian Compressive Sensing Using Laplace Priors (2010, methodology): “In this section, we present a comparison between the proposed method and a number of existing methods on a widely used experimental setup, namely the multiscale CS reconstruction [ 30 ] of the 512 512 Mondrian image.”
• Compressed sensing based compression of SAR raw data (2009, background): “The second one is inspired by the socalled “hybrid compressed sensing” proposed in [17].”
• Challenges of Big Data Analysis (2013, neutral): “9.”
• 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.”
• Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit (2012, background): “Some of the rapidly accumulating literature documenting this phenomenon includes [8], [16], [18], [20], [21], [32], [48], [50], [51], [55]–[58].”
• Enhancing Sparsity by Reweighted ℓ1 Minimization (2007, background): “ deal very effectively (a) with only approximately sparse signals and (b) with measurement noise. The implications of these facts are quite farreaching, with potential applications in data compression [24,28], digital photography [29], medical imaging [23,30], error correction [31,32], analog-to-digi”
• A Survey of Sparse Representation: Algorithms and Applications (2015, background): “All these literature [11–17] laid the foundation of CS theory and provided the theoretical basis for future research.”
• Counting faces of randomly-projected polytopes when the projection radically lowers dimension (2006, background): “) The interested reader may pursue the papers of Candès and collaborators, [4, 6], other theoretical work [28, 20, 31] and much recent applied work [32, 14].”
• Sparsity- and continuity-promoting seismic image recovery with curvelet frames (2008, methodology): “After discretization, the nonlinear optimization problem for the seismic amplitude recovery (see, e.g., [13,18, 48 ]) has the following form:”
• Sparse MRI: The application of compressed sensing for rapid MR imaging (2007, methodology): “Even when using other sparsifying transforms in the objective, it is often useful to include a TV penalty as well (27).”
• Multitask Compressive Sensing (2009, methodology): “5(a) is from [48] and the other two images Fig.”
• Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse (2008, background): “Partial Fourier matrices and partial Hadamard matrices have drawn considerable attention in the sparse approximation community [7], [6], [55], [54], [31].”
• 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.”
• Inpainting and Zooming Using Sparse Representations (2009, methodology): “Additionally, we would like to make a connection with the emerging theory which goes by the name of “compressive sampling” or “compressed sensing” as recently developed by Donoho et al. [32, 33 ] and Cand`es et al. [34, 35, 36].”