pith. sign in

arxiv: 2402.15944 · v3 · submitted 2024-02-25 · 💻 cs.IT · eess.SP· math.IT

On A Class of Greedy Sparse Recovery Algorithms

Gang Li , Qiuwei Li , Shuang Li , Wu Angela Li This is my paper

Pith reviewed 2026-05-24 03:23 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords sparse signal recoverygreedy algorithmsorthogonal matching pursuitbasis pursuitunderdetermined linear systemscompressive sensingl1 minimization
0
0 comments X

The pith

A characterization of solutions to vx = Q vs enables greedy sparse recovery algorithms that outperform classical OMP and basis pursuit.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a novel greedy method for finding the sparsest solution to an under-determined linear system by first characterizing all solutions to vx = Q vs. This characterization lets the recovery operate directly in the vs-space using a chosen measure such as l2 or l1. An OMP-type algorithm based on the l2 measure is derived that improves recovery accuracy over standard OMP while keeping similar computational cost. A separate l1-based procedure called Alg_GL1 is shown to exceed the performance of classical basis pursuit. The same characterization also supports variants that incorporate CoSaMP-style atom selection, with numerical tests on synthetic data and images confirming gains in accuracy and stability.

Core claim

By using a characterization of solutions to the under-determined system vx = Q vs, sparse recovery can be performed directly in the vs-space with a chosen measure. With an l2-based measure an OMP-type algorithm is obtained that significantly outperforms classical OMP in recovery accuracy at comparable complexity. An l1-based algorithm denoted Alg_GL1 is derived that significantly outperforms classical basis pursuit. Combining the approach with the CoSaMP strategy produces a broader class of high-performance greedy algorithms, all of which demonstrate improved accuracy and robustness to matrix instability and measurement noise.

What carries the argument

The characterization of solutions to vx = Q vs that permits direct sparse recovery in the vs-space using a chosen l2 or l1 measure without further hidden assumptions on Q or the support.

If this is right

  • The l2-based OMP-type algorithm recovers sparse signals with higher accuracy than classical OMP at comparable computational cost.
  • The l1-based Alg_GL1 algorithm recovers sparse signals with higher accuracy than classical basis pursuit.
  • Variants that combine the characterization with CoSaMP atom selection form a class of greedy algorithms with further accuracy gains.
  • The methods remain effective under numerical instability in Q and additive disturbance in vx.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The direct vs-space formulation may allow simpler proofs of exact recovery conditions for other greedy procedures.
  • The same characterization could support recovery with measures other than l2 and l1 that trade off sparsity against different noise models.
  • Because the approach works without extra assumptions on Q, it may apply to sensing matrices that violate standard restricted isometry requirements.

Load-bearing premise

The characterization of solutions to the under-determined system permits direct sparse recovery in the vs-space without additional hidden assumptions on the matrix Q or the support.

What would settle it

If standard benchmark experiments show the new OMP-type and Alg_GL1 algorithms fail to exceed the recovery accuracy of classical OMP and basis pursuit on the same problem instances, the performance claims would be refuted.

Figures

Figures reproduced from arXiv: 2402.15944 by Gang Li, Qiuwei Li, Shuang Li, Wu Angela Li.

Figure 1
Figure 1. Figure 1: The rate ϱok of successful recovery and the wall-clock time Tc with respect to different κ for each of the ten algorithms for N = 64, L = 128, J = 1000. 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0 0.2 0.4 0.6 0.8 1 OMPC IRLSC AlgGL2 AlgGLQ AlgGLQ F (a) 0.25 0.3 0.35 0.4 0.45 0.5 0.55 101 102 103 OMPC IRLSC AlgGL2 AlgGLQ AlgGLQ F (b) [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The rate ϱok of successful recovery and the wall-clock time Tc with respect to different κ for each of the five algorithms for N = 256, L = 512, J = 100. rithm significantly outperforms the other four algorithms in terms of successful recovery rates. In addition, its accelerated version, AlgF GLQ, achieves a slightly higher successful recovery rate compared to IRLSC , as shown in [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 3
Figure 3. Figure 3: The rate of successful recovery ϱok with respect to a series of sparsity level κ and signal dimension N. These phase transition plots are generated with J = 100 samples and with the setting (κ, N, L = 2N). 101 102 103 104 105 0 0.2 0.4 0.6 0.8 1 OMPC IRLSC AlgGL2 AlgGLQ AlgGLQ F (a) 101 102 103 104 105 100 102 104 OMPC IRLSC AlgGL2 AlgGLQ AlgGLQ F (b) [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The rate ϱok of successful recovery and the wall-clock time Tc with respect to CQ for each of the five algorithms for κ = 25, N = 256, L = 512 and J = 100. IRLSC encounters numerical issues and fails to work properly; 2) the conditioning number CQ has almost no effect on the performance of the three of our proposed algorithms in terms of ϱok and Tc. This is fur￾ther confirmed under the setting (κ, N, L) = … view at source ↗
Figure 5
Figure 5. Figure 5: The rate ϱok of successful recovery and the wall-clock time Tc with respect to CQ for each of the five algorithms for κ = 60, N = 512, L = 1024 and J = 100. 103 104 105 106 107 108 109 1010 20 40 60 80 100 120 140 AlgGL2 AlgGLQ AlgGLQ F [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The wall-clock time Tc of the three algorithms with respect to CQ for κ = 500, N = 2048, L = 4096 and J = 10. 5.3 Robustness against low-rank disturbance Next, we evaluate the performance of our proposed algorithms under the noisy signal model introduced in Section 4.3, with a particular focus on comparing them to IRLSC . 5.3.1 Synthetic data We repeat the previous experiments with parameters N = 128, L = … view at source ↗
Figure 7
Figure 7. Figure 7: The rate ϱok of successful recovery and the wall-clock time Tc with respect to different noise variance σ for each of the three algorithms for N = 128, L = 256, J = 100. MRI1 Clean Noisy OMPC IRLSC AlgGL1 AlgF GL1 AlgGLQ AlgF GLQ MRI2 [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Image reconstruction by the six algorithms: OMP [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
read the original abstract

Sparse signal recovery deals with finding the sparsest solution of an under-determined linear system $\vx = \mQ\vs$. In this paper, we propose a novel greedy approach to addressing the challenges from such a problem. Such an approach is based on a characterization of solutions to the system, which allows us to work on the sparse recovery in the $\vs$-space directly with a given measure. With $l_2$-based measure, an orthogonal matching pursuit (OMP)-type algorithm is proposed, which significantly outperforms the classical OMP algorithm in terms of recovery accuracy while maintaining comparable computational complexity. An $l_1$-based algorithm, denoted as $\text{Alg}_{GL1}$, is derived. Such an algorithm significantly outperforms the classical basis pursuit (BP) algorithm. Combining with the CoSaMP-strategy for selecting atoms, a class of high performance greedy algorithms is also derived. Extensive numerical simulations on both synthetic and image data are carried out, with which the superior performance of our proposed algorithms is demonstrated in terms of sparse recovery accuracy and robustness against numerical instability of the system matrix $\mQ$ and disturbance in the measurement $\vx$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims to introduce a novel greedy approach for sparse signal recovery from under-determined linear systems vx = Q vs, based on a characterization of solutions that permits direct application of l2 or l1 measures in the vs-space. This yields an OMP-type algorithm claimed to significantly outperform classical OMP in recovery accuracy at comparable complexity, an l1-based Alg_GL1 claimed to outperform basis pursuit, and a broader class obtained by combining with the CoSaMP atom-selection strategy. Superior performance and robustness to matrix instability and measurement noise are asserted on the basis of extensive numerical simulations on synthetic and image data.

Significance. If the characterization is shown to be equivalent (or the induced measure provably preserves the original recovery objective) and the empirical gains are reproducible with proper controls, the work could supply practical algorithms with improved accuracy for compressed sensing tasks. The direct-vs-space formulation and robustness emphasis address real implementation concerns.

major comments (2)
  1. [Section 2/3 (characterization of solutions)] Characterization of solutions (Section 2/3, around the derivation of the vs-space measure): the claim that this characterization 'allows us to work on the sparse recovery in the vs-space directly with a given measure' is load-bearing for both the OMP-type and Alg_GL1 algorithms. It is not shown whether the transformation (e.g., via left-multiplication, pseudo-inverse, or auxiliary system) yields an equivalent objective to the original l0 problem for arbitrary under-determined Q; without explicit conditions on rank(Q), null-space structure, or support, the asserted superiority over classical OMP and BP cannot be guaranteed.
  2. [Numerical simulations section] Numerical experiments (Section on simulations, Tables/Figures reporting recovery rates): the central empirical claim of 'significantly outperforms' is supported only by simulations whose design details (Monte Carlo trial count, statistical testing, error bars, data exclusion criteria, exact matrix dimensions and sparsity levels) are insufficiently specified. This undermines the quantitative comparison to OMP and BP.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'extensive numerical simulations' could be accompanied by one sentence summarizing key experimental parameters (e.g., problem dimensions, number of trials) to give readers immediate context.
  2. [Notation and preliminaries] Notation: ensure that vector/matrix boldface and the symbols vx, vs, Q are used consistently from the first equation onward.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The two major comments identify areas where additional rigor and transparency will strengthen the manuscript. We address each point below and will revise accordingly.

read point-by-point responses

  1. Referee: Characterization of solutions (Section 2/3, around the derivation of the vs-space measure): the claim that this characterization 'allows us to work on the sparse recovery in the vs-space directly with a given measure' is load-bearing for both the OMP-type and Alg_GL1 algorithms. It is not shown whether the transformation (e.g., via left-multiplication, pseudo-inverse, or auxiliary system) yields an equivalent objective to the original l0 problem for arbitrary under-determined Q; without explicit conditions on rank(Q), null-space structure, or support, the asserted superiority over classical OMP and BP cannot be guaranteed.

    Authors: We agree that the equivalence between the vs-space measure and the original l0 objective requires explicit justification. The current derivation relies on properties of the linear system, but the manuscript does not fully delineate the conditions (e.g., rank of Q or null-space restrictions) under which the transformed measure preserves the recovery goal. In the revision we will add a dedicated paragraph or subsection stating these conditions and clarifying when the vs-space formulation is equivalent, thereby supporting the performance claims more rigorously. revision: yes

  2. Referee: Numerical experiments (Section on simulations, Tables/Figures reporting recovery rates): the central empirical claim of 'significantly outperforms' is supported only by simulations whose design details (Monte Carlo trial count, statistical testing, error bars, data exclusion criteria, exact matrix dimensions and sparsity levels) are insufficiently specified. This undermines the quantitative comparison to OMP and BP.

    Authors: We concur that the simulation section lacks sufficient methodological detail for reproducibility. The revised manuscript will specify the exact number of Monte Carlo trials per configuration, include error bars or standard deviations on all reported recovery rates, list precise matrix dimensions and sparsity levels, describe any data exclusion rules, and add statistical comparisons where appropriate. These additions will make the empirical superiority claims more credible and verifiable. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation rests on stated characterization of solutions without self-referential reduction

full rationale

The paper presents its core approach as based on an (unspecified in abstract) characterization of solutions to vx = Q vs that permits direct sparse recovery in vs-space using l2 or l1 measures. No equations, self-citations, or fitted parameters are shown reducing the claimed OMP-type or Alg_GL1 algorithms to their own inputs by construction. Outperformance claims are tied to numerical simulations on synthetic and image data rather than any definitional equivalence. This matches the default expectation of a non-circular paper; the characterization functions as an external premise rather than a self-defined loop.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the central claim rests on an unspecified characterization of solutions whose details are not provided.

pith-pipeline@v0.9.0 · 5734 in / 1145 out tokens · 28178 ms · 2026-05-24T03:23:48.229638+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

66 extracted references · 66 canonical work pages

  1. [1]

    Sparse recovery.Mathemat- ical Foundations of Big Data Analytics , pages 131–148, 2021

    Vladimir Shikhman, David M¨ uller, Vladimir Shikhman, and David M¨ uller. Sparse recovery.Mathemat- ical Foundations of Big Data Analytics , pages 131–148, 2021

    work page 2021

  2. [2]

    Sparse recovery for scientific data

    Stanley Osher. Sparse recovery for scientific data. Technical report, Univ. of California, Los Angeles, CA (United States), 2019

    work page 2019

  3. [3]

    A tutorial on sparse signal reconstruction and its applications in signal processing

    Ljubiˇ sa Stankovi´ c, Ervin Sejdi´ c, Srdjan Stankovi´ c, Miloˇ s Dakovi´ c, and Irena Orovi´ c. A tutorial on sparse signal reconstruction and its applications in signal processing. Circuits, Systems, and Signal Processing, 38:1206–1263, 2019

    work page 2019

  4. [4]

    Atomic norm denoising for complex exponentials with unknown waveform modulations

    Shuang Li, Michael B Wakin, and Gongguo Tang. Atomic norm denoising for complex exponentials with unknown waveform modulations. IEEE Transactions on Information Theory , 66(6):3893–3913, 2019

    work page 2019

  5. [5]

    Rank awareness in joint sparse recovery

    Mike E Davies and Yonina C Eldar. Rank awareness in joint sparse recovery. IEEE Transactions on Information Theory, 58(2):1135–1146, 2012

    work page 2012

  6. [6]

    Jointly sparse signal recovery with prior info

    Natalie Durgin, Rachel Grotheer, Chenxi Huang, Shuang Li, Anna Ma, Deanna Needell, and Jing Qin. Jointly sparse signal recovery with prior info. In 2019 53rd Asilomar Conference on Signals, Systems, and Computers, pages 645–649. IEEE, 2019

    work page 2019

  7. [7]

    Limits on support recovery of sparse signals via multiple-access communication techniques

    Yuzhe Jin, Young-Han Kim, and Bhaskar D Rao. Limits on support recovery of sparse signals via multiple-access communication techniques. IEEE Transactions on Information Theory , 57(12):7877– 7892, 2011

    work page 2011

  8. [8]

    Xing Zhang, Haiyang Zhang, and Yonina C. Eldar. Near-field sparse channel representation and esti- mation in 6G wireless communications. IEEE Transactions on Communications , 72(1):450–464, 2023

    work page 2023

  9. [9]

    Adaptive interference cancellation using atomic norm minimization and denoising

    Shuang Li, Daniel Gaydos, Payam Nayeri, and Michael B Wakin. Adaptive interference cancellation using atomic norm minimization and denoising. IEEE Antennas and Wireless Propagation Letters , 19(12):2349–2353, 2020. 20

    work page 2020

  10. [10]

    Yong Huang, James L Beck, Stephen Wu, and Hui Li. Bayesian compressive sensing for approximately sparse signals and application to structural health monitoring signals for data loss recovery.Probabilistic Engineering Mechanics, 46:62–79, 2016

    work page 2016

  11. [11]

    Atomic norm minimization for modal analysis from random and compressed samples

    Shuang Li, Dehui Yang, Gongguo Tang, and Michael B Wakin. Atomic norm minimization for modal analysis from random and compressed samples. IEEE Transactions on Signal Processing , 66(7):1817– 1831, 2018

    work page 2018

  12. [12]

    Group sparsity-aware convolutional neural network for continuous missing data recovery of structural health monitoring

    Zhiyi Tang, Yuequan Bao, and Hui Li. Group sparsity-aware convolutional neural network for continuous missing data recovery of structural health monitoring. Structural Health Monitoring , 20(4):1738–1759, 2021

    work page 2021

  13. [13]

    Hyperspectral image compressed sensing via low- rank and joint-sparse matrix recovery

    Mohammad Golbabaee and Pierre Vandergheynst. Hyperspectral image compressed sensing via low- rank and joint-sparse matrix recovery. In 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , pages 2741–2744. IEEE, 2012

    work page 2012

  14. [14]

    Sparse recovery of hyperspectral signal from natural RGB images

    Boaz Arad and Ohad Ben-Shahar. Sparse recovery of hyperspectral signal from natural RGB images. In Computer Vision–ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, October 11–14, 2016, Proceedings, Part VII 14 , pages 19–34. Springer, 2016

    work page 2016

  15. [15]

    Fast hyperspectral diffuse optical imaging method with joint sparsity

    Natalie Durgin, Rachel Grotheer, Chenxi Huang, Shuang Li, Anna Ma, Deanna Needell, and Jing Qin. Fast hyperspectral diffuse optical imaging method with joint sparsity. In2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) , pages 4758–4761. IEEE, 2019

    work page 2019

  16. [16]

    Deep learning

    Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521(7553):436–444, 2015

    work page 2015

  17. [17]

    Deep Learning

    Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning. MIT press, 2016

    work page 2016

  18. [18]

    Compressed sensing

    David L Donoho. Compressed sensing. IEEE Transactions on Information Theory , 52(4):1289–1306, 2006

    work page 2006

  19. [19]

    An introduction to compressive sampling

    Emmanuel J Cand` es and Michael B Wakin. An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2):21–30, 2008

    work page 2008

  20. [20]

    Structured compressed sensing: From theory to applications

    Marco F Duarte and Yonina C Eldar. Structured compressed sensing: From theory to applications. IEEE Transactions on Signal Processing , 59(9):4053–4085, 2011

    work page 2011

  21. [21]

    On collaborative compressive sensing systems: The framework, design, and algorithm

    Zhihui Zhu, Gang Li, Jiajun Ding, Qiuwei Li, and Xiongxiong He. On collaborative compressive sensing systems: The framework, design, and algorithm. SIAM Journal on Imaging Sciences , 11(2):1717–1758, 2018

    work page 2018

  22. [22]

    Roman Vershynin, Y. C. Eldar, and Gitta Kutyniok. Introduction to the non-asymptotic analysis of random matrices. In Y. C. Eldar and G. Kutyniok, editors, Compressed Sensing: Theory and Applications. Cambridge University Press, UK, 2012

    work page 2012

  23. [23]

    A Mathematical Introduction to Compressive Sensing

    Simon Foucart and Holger Rauhut. A Mathematical Introduction to Compressive Sensing . Birkh¨ auser New York, NY, 2013

    work page 2013

  24. [24]

    Feature selection based on struc- tured sparsity: A comprehensive study

    Jie Gui, Zhenan Sun, Shuiwang Ji, Dacheng Tao, and Tieniu Tan. Feature selection based on struc- tured sparsity: A comprehensive study. IEEE Transactions on Neural Networks and Learning Systems , 28(7):1490–1507, 2016

    work page 2016

  25. [25]

    Sparse neural additive model: Interpretable deep learning with feature selection via group sparsity

    Shiyun Xu, Zhiqi Bu, Pratik Chaudhari, and Ian J Barnett. Sparse neural additive model: Interpretable deep learning with feature selection via group sparsity. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases , pages 343–359. Springer, 2023. 21

    work page 2023

  26. [26]

    Imagenet classification with deep convolutional neural networks

    Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Advances in Neural Information Processing Systems , 25, 2012

    work page 2012

  27. [27]

    Sparse convolutional neural networks

    Baoyuan Liu, Min Wang, Hassan Foroosh, Marshall Tappen, and Marianna Pensky. Sparse convolutional neural networks. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pages 806–814, 2015

    work page 2015

  28. [28]

    Regularization paths for generalized linear models via coordinate descent

    Jerome Friedman, Trevor Hastie, and Rob Tibshirani. Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software , 33(1):1, 2010

    work page 2010

  29. [29]

    Structured optimal graph based sparse feature extraction for semi-supervised learning

    Zhonghua Liu, Zhihui Lai, Weihua Ou, Kaibing Zhang, and Ruijuan Zheng. Structured optimal graph based sparse feature extraction for semi-supervised learning. Signal Processing, 170:107456, 2020

    work page 2020

  30. [30]

    Optimally sparse representation in general (nonorthogonal) dictio- naries via ℓ1 minimization

    David L Donoho and Michael Elad. Optimally sparse representation in general (nonorthogonal) dictio- naries via ℓ1 minimization. Proceedings of the National Academy of Sciences , 100(5):2197–2202, 2003

    work page 2003

  31. [31]

    Decoding by linear programming

    Emmanuel J Cand` es and Terence Tao. Decoding by linear programming. IEEE Transactions on Infor- mation Theory, 51(12):4203–4215, 2005

    work page 2005

  32. [32]

    Atomic decomposition by basis pursuit

    Scott Shaobing Chen, David L Donoho, and Michael A Saunders. Atomic decomposition by basis pursuit. SIAM Review, 43(1):129–159, 2001

    work page 2001

  33. [33]

    Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm

    Irina F Gorodnitsky and Bhaskar D Rao. Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm. IEEE Transactions on Signal Processing, 45(3):600–616, 1997

    work page 1997

  34. [34]

    An affine scaling methodology for best basis selection

    Bhaskar D Rao and Kenneth Kreutz-Delgado. An affine scaling methodology for best basis selection. IEEE Transactions on Signal Processing , 47(1):187–200, 1999

    work page 1999

  35. [35]

    Iteratively reweighted least squares minimization for sparse recovery

    Ingrid Daubechies, Ronald DeVore, Massimo Fornasier, and C Sinan G¨ unt¨ urk. Iteratively reweighted least squares minimization for sparse recovery. Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences , 63(1):1–38, 2010

    work page 2010

  36. [36]

    Two-level ℓ1 mini- mization for compressed sensing

    Xiaolin Huang, Yipeng Liu, Lei Shi, Sabine Van Huffel, and Johan AK Suykens. Two-level ℓ1 mini- mization for compressed sensing. Signal Processing, 108:459–475, 2015

    work page 2015

  37. [37]

    Enhancing sparsity by reweighted ℓ1 minimization

    Emmanuel J Candes, Michael B Wakin, and Stephen P Boyd. Enhancing sparsity by reweighted ℓ1 minimization. Journal of Fourier Analysis and Applications , 14:877–905, 2008

    work page 2008

  38. [38]

    Sparse signal reconstruction via iterative support detection

    Yilun Wang and Wotao Yin. Sparse signal reconstruction via iterative support detection. SIAM Journal on Imaging Sciences , 3(3):462–491, 2010

    work page 2010

  39. [39]

    Iteratively reweighted algorithms for compressive sensing

    Rick Chartrand and Wotao Yin. Iteratively reweighted algorithms for compressive sensing. In 2008 IEEE International Conference on Acoustics, Speech and Signal Processing , pages 3869–3872. IEEE, 2008

    work page 2008

  40. [40]

    Atomic decomposition by basis pursuit

    Scott Shaobing Chen, David L Donoho, and Michael A Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing , 20(1):33–61, 1998

    work page 1998

  41. [41]

    Regression shrinkage and selection via the lasso

    Robert Tibshirani. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B: Statistical Methodology , 58(1):267–288, 1996

    work page 1996

  42. [42]

    A fast iterative shrinkage-thresholding algorithm for linear inverse problems

    Amir Beck and Marc Teboulle. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences , 2(1):183–202, 2009

    work page 2009

  43. [43]

    Learning to invert: Signal recovery via deep convolutional networks

    Ali Mousavi and Richard G Baraniuk. Learning to invert: Signal recovery via deep convolutional networks. In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 2272–2276. IEEE, 2017. 22

    work page 2017

  44. [44]

    Matching pursuits with time-frequency dictionaries

    St´ ephane G Mallat and Zhifeng Zhang. Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 41(12):3397–3415, 1993

    work page 1993

  45. [45]

    Greed is good: Algorithmic results for sparse approximation

    Joel A Tropp. Greed is good: Algorithmic results for sparse approximation. IEEE Transactions on Information Theory, 50(10):2231–2242, 2004

    work page 2004

  46. [46]

    Gradient pursuits

    Thomas Blumensath and Mike E Davies. Gradient pursuits. IEEE Transactions on Signal Processing , 56(6):2370–2382, 2008

    work page 2008

  47. [47]

    Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit

    David L Donoho, Yaakov Tsaig, Iddo Drori, and Jean-Luc Starck. Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Transactions on Informa- tion Theory, 58(2):1094–1121, 2012

    work page 2012

  48. [48]

    CoSaMP: Iterative signal recovery from incomplete and inaccurate samples

    Deanna Needell and Joel A Tropp. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis , 26(3):301–321, 2009

    work page 2009

  49. [49]

    Stagewise weak gradient pursuits

    Thomas Blumensath and Mike E Davies. Stagewise weak gradient pursuits. IEEE Transactions on Signal Processing, 57(11):4333–4346, 2009

    work page 2009

  50. [50]

    Greedy algorithms for compressed sensing

    Thomas Blumensath, Michael E Davies, and Gabriel Rilling. Greedy algorithms for compressed sensing. In Y. C. Eldar and G. Kutyniok, editors, Compressed Sensing: Theory and Applications . Cambridge University Press, UK, 2012

    work page 2012

  51. [51]

    Grassmannian frames with applications to coding and communication

    Thomas Strohmer and Robert W Heath Jr. Grassmannian frames with applications to coding and communication. Applied and Computational Harmonic Analysis , 14(3):257–275, 2003

    work page 2003

  52. [52]

    Optimized projections for compressed sensing

    Michael Elad. Optimized projections for compressed sensing. IEEE Transactions on Signal Processing, 55(12):5695–5702, 2007

    work page 2007

  53. [53]

    On projection matrix optimization for compressive sensing systems

    Gang Li, Zhihui Zhu, Dehui Yang, Liping Chang, and Huang Bai. On projection matrix optimization for compressive sensing systems. IEEE Transactions on Signal Processing , 61(11):2887–2898, 2013

    work page 2013

  54. [54]

    Projection design for statistical compressive sensing: A tight frame based approach

    Wei Chen, Miguel RD Rodrigues, and Ian J Wassell. Projection design for statistical compressive sensing: A tight frame based approach. IEEE Transactions on Signal Processing , 61(8):2016–2029, 2013

    work page 2016

  55. [55]

    Designing structured tight frames via an alternating projection method

    Joel A Tropp, Inderjit S Dhillon, Robert W Heath, and Thomas Strohmer. Designing structured tight frames via an alternating projection method. IEEE Transactions on Information Theory, 51(1):188–209, 2005

    work page 2005

  56. [56]

    Optimal tight frames and quantum measurement

    Yonina C Eldar and G David Forney. Optimal tight frames and quantum measurement. IEEE Trans- actions on Information Theory , 48(3):599–610, 2002

    work page 2002

  57. [57]

    Construction of incoherent unit norm tight frames with application to compressed sensing

    Evaggelia V Tsiligianni, Lisimachos P Kondi, and Aggelos K Katsaggelos. Construction of incoherent unit norm tight frames with application to compressed sensing. IEEE Transactions on Information Theory, 60(4):2319–2330, 2014

    work page 2014

  58. [58]

    Revisiting sparse error correction: model analysis and new algorithms

    Gang Li, Xiao Li, and Wu Angela Li. Revisiting sparse error correction: model analysis and new algorithms. Available at SSRN 5069675 , 2024

    work page 2024

  59. [59]

    Structured sparse representation with low-rank interference

    Minh Dao, Yuanming Suo, Sang Peter Chin, and Trac D Tran. Structured sparse representation with low-rank interference. In 2014 48th Asilomar Conference on Signals, Systems and Computers , pages 106–110. IEEE, 2014

    work page 2014

  60. [60]

    Gpr target detection by joint sparse and low-rank matrix decomposition.IEEE Transactions on Geoscience and Remote Sensing, 57(5):2583–2595, 2018

    Fok Hing Chi Tivive, Abdesselam Bouzerdoum, and Canicious Abeynayake. Gpr target detection by joint sparse and low-rank matrix decomposition.IEEE Transactions on Geoscience and Remote Sensing, 57(5):2583–2595, 2018. 23

    work page 2018

  61. [61]

    Robust principal component analysis? Journal of the ACM (JACM) , 58(3):1–37, 2011

    Emmanuel J Cand` es, Xiaodong Li, Yi Ma, and John Wright. Robust principal component analysis? Journal of the ACM (JACM) , 58(3):1–37, 2011

    work page 2011

  62. [62]

    Godec: Randomized low-rank & sparse matrix decomposition in noisy case

    Tianyi Zhou and Dacheng Tao. Godec: Randomized low-rank & sparse matrix decomposition in noisy case. In Proceedings of the 28th International Conference on Machine Learning, ICML 2011 , 2011

    work page 2011

  63. [63]

    Low-rank plus sparse matrix decomposi- tion for accelerated dynamic mri with separation of background and dynamic components

    Ricardo Otazo, Emmanuel Candes, and Daniel K Sodickson. Low-rank plus sparse matrix decomposi- tion for accelerated dynamic mri with separation of background and dynamic components. Magnetic Resonance in Medicine, 73(3):1125–1136, 2015

    work page 2015

  64. [64]

    Near-optimal estimation of simultaneously sparse and low-rank matrices from nested linear measurements

    Sohail Bahmani and Justin Romberg. Near-optimal estimation of simultaneously sparse and low-rank matrices from nested linear measurements. Information and Inference: A Journal of the IMA , 5(3):331– 351, 2016

    work page 2016

  65. [65]

    Compressive principal component pursuit

    John Wright, Arvind Ganesh, Kerui Min, and Yi Ma. Compressive principal component pursuit. In- formation and Inference: A Journal of the IMA , 2(1):32–68, 2013

    work page 2013

  66. [66]

    Amp-inspired deep networks for sparse linear inverse problems

    Mark Borgerding, Philip Schniter, and Sundeep Rangan. Amp-inspired deep networks for sparse linear inverse problems. IEEE Transactions on Signal Processing , 65(16):4293–4308, 2017. 24

    work page 2017