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Deep greedy unfolding: Sorting out argsorting in greedy sparse recovery algorithms

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Softsort unrolls greedy sparse recovery into trainable networks with exact error control.

desk verdict Honest and useful unrolling paper: the OMP half is solid, the IHT approximation theorem is not proven for the step sizes used in the experiments, but the gap looks fixable. read the letter →

arxiv 2505.15661 v1 pith:CEPISEEY submitted 2025-05-21 cs.LG cs.NAcs.NEmath.NA

Sina Mohammad-Taheri , Matthew J. Colbrook , Simone Brugiapaglia This is my paper · ORCID
classification cs.LGcs.NAcs.NEmath.NA MSC 68T0794A1265F22
keywords sparserecoveryalgorithmunrollingorthogonalmatchingpursuititerativehardthresholdingsoftsortdifferentiablesortingneuralnetworksstructuredsparsity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper shows that two classic greedy sparse-recovery algorithms, OMP and IHT, can be made differentiable without losing control over accuracy. The trick is to replace the hard argsort step, the piecewise-constant operation that blocks gradient flow, with softsort, a smooth permutation-matrix relaxation governed by a temperature parameter $\tau$. The authors prove that for $\tau$ small enough relative to the gaps between sorted magnitudes, the soft trajectories stay within any prescribed $\epsilon$ of the exact OMP and IHT trajectories (Theorems 3.6 and 3.9). This turns unrolling of greedy algorithms into a rigorous, trainable network design, and the paper demonstrates numerically that the resulting OMP-Net and IHT-Net can outperform the classical algorithms in heavily undersampled structured recovery.

What carries the argument

The central object is softsort, a continuous relaxation of argsort that maps a vector $v\in\mathbb{R}^N$ to a row-stochastic matrix $\tilde{P}_{\text{argsort}}(v) = \text{softmax}(-|\text{sort}(v)\mathbf{1}^\top - \mathbf{1}v^\top|/\tau)$, whose rows approximate the one-hot rows of the exact permutation matrix with a temperature parameter $\tau$ controlling sharpness. The paper re-expresses OMP as projection-based pOMP and IHT as pIHT, both built from permutation matrices, then substitutes the soft surrogate. The proofs hinge on a Lipschitz property of softsort (Proposition 3.3), a bound on how quickly the soft permutation matrix converges to the exact one (Lemma B.2), and sensitivity analysis of least squares (Lemma B.1) for OMP, or a one-step perturbation bound for the hard-thresholding mask (Lemma C.1) for IHT.

What would settle it

Run OMP and Soft-OMP on a constructed instance where, at some iteration, the two largest entries of $|A^*(y-Ax^{(n)})|$ are exactly equal or differ by less than $2\|A\|\epsilon$; then the row-wise argmax of the soft permutation matrix will not match OMP's selection and the $\epsilon$-accuracy guarantee of Theorem 3.6 fails, showing visible divergence between the iterates. The same check applies to IHT by making two entries of $|u|$ closer than $2L\epsilon$.

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Extended reading notes

Core claim

Soft-OMP and Soft-IHT are differentiable counterparts of OMP and IHT that approximate them with controllable accuracy: for iteration counts up to $n$, if the temperature satisfies $\tau \le (g^{(1:n)} - 2\|A\|\epsilon)/\log(C/\epsilon)$ for OMP or $\tau \le (g^{(1:n)} - 2L\epsilon)/\log(C/\epsilon)$ for IHT, then the maximum deviation between soft and exact iterates stays below $\epsilon$. The min-gap $g^{(1:n)}$ is the separation between the largest and remaining sorted magnitudes in OMP, and between all magnitudes in IHT. Consequently, unrolled networks built from these soft algorithms inherit recovery guarantees, and with trainable weight vectors they learn latent support structure and beat classical OMP and IHT by orders of magnitude in undersampled, structured experiments.

Load-bearing premise

The bounds collapse if at any iteration the gap between the top magnitude and the next one (OMP) or between any two magnitudes (IHT) becomes zero or very small, because the theorem's condition that $\tau$ be small relative to that gap cannot be met.

Editorial extensions

If this is right

  • OMP and IHT can be unrolled into deep networks with rigorous approximation guarantees, closing the differentiability gap that previously forced ad-hoc engineering fixes.
  • OMP-Net and IHT-Net, trained with weight-sharing on structure-aware weights, recover signals near the noise floor in undersampled regimes ($m=22$ for OMP, $m=36$ for IHT with $N=256$) where classical OMP and IHT fail.
  • Because $\|\tilde{x} - x\| \le \|\tilde{x} - x^{(n)}\| + \|x^{(n)} - x\|$, classical recovery guarantees for OMP and IHT transfer to the soft algorithms (Remark 3.8).
  • The temperature $\tau$ is a knob trading approximation accuracy (small $\tau$) against gradient flow and trainability (larger $\tau$); numerical experiments place the sweet spot in the transition region of the accuracy curve.
  • Learned weights capture the latent set $T$ containing the support, providing interpretable structure extraction from data rather than just a black-box improvement.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same permutation-proxy recipe could be applied to other argsort-based greedy solvers such as CoSaMP or subspace pursuit; the paper lists these as future candidates, and the error analysis would follow the same pattern with a different perturbation term.
  • The min-gap assumption is data-dependent, so in adversarial or exactly-tied settings the guarantee disappears; in practice ties are rare due to round-off, but a tie-breaking or gap-regularized variant could make the method robust to near-ties.
  • Because the bounds' constants involve properties like the restricted isometry constant and coherence, the theoretical regime may be far more conservative than the observed performance, so the practical range of $\tau$ may extend well beyond the proven range.
  • Making $\tau$ itself a trainable parameter or a per-layer schedule could balance the accuracy-gradient trade-off dynamically, an extension the paper does not explore.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper proposes differentiable relaxations of two greedy sparse recovery algorithms, OMP and IHT, by replacing the non-differentiable argsort operation with softsort-based approximate permutation matrices. It defines Soft-OMP and Soft-IHT, states approximation theorems (Theorems 3.6 and 3.9) bounding the distance to the exact algorithms in terms of the softsort temperature tau and certain min-gaps, and unrolls the soft algorithms into trainable OMP-Net and IHT-Net architectures. Numerical experiments validate the tau-asymptotic behavior and demonstrate that learned structure-aware weights can outperform the classical algorithms in a structured undersampled recovery task.

Significance. If the results hold, this is a valuable contribution to algorithm unrolling for greedy sparse recovery: it gives a principled, differentiable replacement for the discontinuous argsort operator with explicit approximation guarantees, rather than relying on ad hoc engineering fixes. The main theorems are not circular: the bounds follow from softsort convergence and least-squares perturbation analysis, not from the trained network weights. The paper also provides detailed appendices and a public code repository, which strengthens reproducibility. The principal caveats are that the guarantees are conditional on data-dependent min-gaps that are not known a priori, and that the IHT guarantee as stated is not actually proved for the general step size used in the experiments; these points are addressed in the major comments.

major comments (2)
  1. [§3.3, Theorem 3.9 and Appendix C, Lemma C.1] Theorem 3.9 is stated for arbitrary step size eta > 0, but the proof in Appendix C only covers eta = 1. Lemma C.1 defines u(x) = (I - A^*A)x + A^*y and sets L = ||I - A^*A||; for general eta the IHT update is u_eta(x) = (I - eta A^*A)x + eta A^*y, whose Lipschitz constant is ||I - eta A^*A|| and whose inhomogeneous term is eta A^*y. The theorem's constant C(n) contains no eta, so the printed argument cannot establish the stated bound. Since the numerical validation in Section 5.1 uses eta = 0.6 and the IHT-Net experiments in Section 5.2 use eta = 0.5, the claimed guarantee is not supported in the demonstrated regime. Please either extend the proof to general eta with constants depending on eta, or restate the theorem and lemma for eta = 1 and adjust the experiments accordingly.
  2. [Appendix B, Lemma B.2 and Theorem 3.6] The proof of Lemma B.2 concludes ||Pi^(n) - tilde-Pi^(n)||_F^2 <= 2n(N-1)^2 e^{-2 tilde-g^(1:n)/tau}; taking square roots gives sqrt(2n)(N-1)e^{-tilde-g^(1:n)/tau}, not sqrt(2n(N-1))e^{-tilde-g^(1:n)/tau}. As a result, the constant C(n) in Theorem 3.6 is too small by a factor of sqrt(N-1) for N > 1. The qualitative exponential-in-tau conclusion remains, but the displayed constant and the sufficient condition on tau must be corrected.
minor comments (5)
  1. [Algorithm 3.4] In the update for tilde-v^(n+1), the right-hand side should read |tilde-u^(n+1)| rather than |u^(n+1)|; the tilde is missing.
  2. [Algorithms 3.3 and 3.4] The input lines list the observation vector as y in C^N; the measurement vector should be in C^m, as in Algorithms 2.1 and 2.2.
  3. [Section 5.1] The notation 'N trial' for the number of trials is inconsistent with the later definition of N_trial; please standardize the notation.
  4. [Theorems 3.6 and 3.9] Both theorems assume positive min-gaps; it would be helpful to state explicitly that the guarantees are vacuous when any tie occurs, since a tie makes g^(i) = 0.
  5. [Abstract and Section 1.1] The phrase 'controllable degree of accuracy' overstates the result because the min-gap is data-dependent and is not known a priori; a phrase such as 'controlled, provided the min-gaps are sufficiently large' would be more precise.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the approximation theorems are explicit bounds on tau; the sole self-citation is contextual and not load-bearing.

full rationale

The central claims, Theorems 3.6 and 3.9, are derived from explicit external ingredients: softsort properties from [38], least-squares sensitivity from [42], RIC/coherence estimates, and Lipschitz analysis of the underlying descent map. The theorems state how small the softsort temperature tau must be relative to the data-dependent min-gaps g^(i) to guarantee a specified accuracy epsilon; no fitted parameter is renamed as a prediction, and no conclusion is used in its own assumption. The only self-citation ([34]) appears in the framing, e.g., "This work is an extension of [34]" and "The present paper builds upon the authors' previous work [34]", but the Appendix proofs for Theorems 3.6 and 3.9 do not invoke [34] as a premise. The skeptic's observations that the proof of Theorem 3.9 only treats eta=1 and that Lemma B.2's constant may be too small are internal rigor/correctness concerns, not circularity: they do not make the claimed result equivalent to its inputs by construction. Accordingly, the paper is substantially self-contained and non-circular; the score of 1 reflects the minor, non-load-bearing self-citation rather than any circular reduction.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The ledger lists the hand-set temperature tau and the IHT step size eta as free parameters, plus the no-ties, normalized-column, RIC, softsort-property, and least-squares-sensitivity axioms. The central approximation theorems are derived rather than fitted, so circularity burden is low.

free parameters (2)
  • softsort temperature tau = 1e-3 in experiments
    Controls the trade-off between approximation accuracy and gradient flow. The theorems impose upper bounds on tau in terms of min-gap and desired epsilon, but in the neural network experiments tau is chosen empirically (Section 5.2).
  • IHT step size eta = 0.6 in Experiment I, 0.5 in Experiment II
    Fixed by hand in experiments; the proof of Theorem 3.9 effectively assumes eta=1, so the theorem as stated does not cover the algorithm as run. This is a gap rather than a fitted parameter.
assumptions (5)
  • domain assumption No ties in the vectors being sorted: v_i != v_j for all i and j
    Assumed in Section 2.3 to make argsort well-defined and min-gaps positive. Violated by ties, but common in compressed sensing due to round-off; the theorems require positive min-gaps.
  • domain assumption A has l2-normalized columns
    Used in OMP and IHT algorithms and in the proofs, e.g., ||a_i||=1 in Lemma C.1 part (b).
  • domain assumption Restricted isometry condition delta_n(A) < 1 in Theorem 3.6
    Ensures the submatrices B^(n) are full rank so the least-squares step is well-posed and sigma_min(A_S) >= sqrt(1-delta_n). Standard in compressive sensing.
  • standard math Softsort properties from Prillo and Eisenschlos [38]
    Quoted as Proposition 3.2, including non-negativity, row-stochasticity, asymptotic convergence, and argmax property. The paper proves only continuity (Proposition 3.3) itself.
  • standard math Least-squares sensitivity bound, Theorem 18.1 of Trefethen and Bau
    Used as Lemma B.1 to bound error propagation through the least-squares step in Soft-OMP.

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Pith. "Pith review of Deep greedy unfolding: Sorting out argsorting in greedy sparse recovery algorithms." pith.science (2026). https://pith.science/paper/CEPISEEY

@misc{pith2026250515661,
  author       = {Pith},
  title        = {Pith review of: Deep greedy unfolding: Sorting out argsorting in greedy sparse recovery algorithms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CEPISEEY}},
  note         = {Machine review of arXiv:2505.15661}
}
read the original abstract

Gradient-based learning imposes (deep) neural networks to be differentiable at all steps. This includes model-based architectures constructed by unrolling iterations of an iterative algorithm onto layers of a neural network, known as algorithm unrolling. However, greedy sparse recovery algorithms depend on the non-differentiable argsort operator, which hinders their integration into neural networks. In this paper, we address this challenge in Orthogonal Matching Pursuit (OMP) and Iterative Hard Thresholding (IHT), two popular representative algorithms in this class. We propose permutation-based variants of these algorithms and approximate permutation matrices using "soft" permutation matrices derived from softsort, a continuous relaxation of argsort. We demonstrate -- both theoretically and numerically -- that Soft-OMP and Soft-IHT, as differentiable counterparts of OMP and IHT and fully compatible with neural network training, effectively approximate these algorithms with a controllable degree of accuracy. This leads to the development of OMP- and IHT-Net, fully trainable network architectures based on Soft-OMP and Soft-IHT, respectively. Finally, by choosing weights as "structure-aware" trainable parameters, we connect our approach to structured sparse recovery and demonstrate its ability to extract latent sparsity patterns from data.

Figures

Figures reproduced from arXiv: 2505.15661 by the authors.

Figure 2
Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 2
Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 2.1
Figure 2.1. First element of the operators sort, softsort, argsort and softargsort applied to the two￾dimensional vector v = (v1, v2), as defined in Equations (2.4), (3.1), and (3.2), shown as a function of v1 for fixed v2 = 1 (τ = 0.25). current support S (n) to form the updated support S (n+1). The next step solves a least-squares problem restricted to the indices in S (n+1). This introduces not only non-differentiability due… view at source ↗
Figures from the paper (5 more)
Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p009_2.png]
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 5.1
Figure 5.1. Figure 5.1: Relative ℓ 2 -error as a function of τ (see Subsection 5.1). Recovery accuracy of (Soft-)OMP on the left and (Soft-)IHT on the right for various iteration counts. To prevent numerical issues with logarithms, we compute E(n) (τ ) + ϵ in practice, where ϵ = 10−12 [PI…
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]
Figure 5.2
Figure 5.2. Figure 5.2: From top to bottom: MSE-Loss, oracle weights, learned weights and relative ℓ 2 -error boxplots for (Soft-)OMP on the left and (Soft-)IHT on the right column (see Subsection 5.2 for futher details). Acknowledgements. SM acknowledges support from MITACS Globalink resea…

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Works this paper leans on

47 extracted references · 41 canonical work pages

  1. [1]

    Adcock, S

    B. Adcock, S. Brugiapaglia, and C. G. Webster , Sparse Polynomial Approximation of High-Dimensional Functions , Society for Industrial and Applied Mathematics, Philadelphia, PA, 2022, https://doi.org/10.1137/1.9781611976885, https://epubs.siam.org/doi/abs/10.1137/1.9781611976885, https://arxiv.org/abs/https://epubs.siam.org/doi/pdf/10.1137/1.9781611976885

    doi:10.1137/1.9781611976885 2022

  2. [2]

    Adcock and A

    B. Adcock and A. C. Hansen , Compressive Imaging: Structure, Sampling, Learning , Cambridge University Press, Cambridge, UK, 2021

    work page 2021

  3. [3]

    Arora and B

    S. Arora and B. Barak , Computational complexity: a modern approach , Cambridge University Press, 2009

    work page 2009

  4. [4]

    Bah and R

    B. Bah and R. Ward , The sample complexity of weighted sparse approximation , IEEE Transactions on Signal Processing, 64 (2016), pp. 3145--3155

    work page 2016

  5. [5]

    Behboodi, H

    A. Behboodi, H. Rauhut, and E. Schnoor , Compressive sensing and neural networks from a statistical learning perspective , in Compressed Sensing in Information Processing, Springer, 2022, pp. 247--277

    work page 2022

  6. [6]

    Blondel, O

    M. Blondel, O. Teboul, Q. Berthet, and J. Djolonga , Fast differentiable sorting and ranking , in International Conference on Machine Learning, PMLR, 2020, pp. 950--959

    work page 2020

  7. [7]

    Blumensath and M

    T. Blumensath and M. E. Davies , Iterative thresholding for sparse approximations , Journal of Fourier analysis and Applications, 14 (2008), pp. 629--654

    work page 2008

  8. [8]

    Multi-level Compressed Sensing Petrov-Galerkin discretization of high-dimensional parametric PDEs

    J.-L. Bouchot, H. Rauhut, and C. Schwab , Multi-level compressed sensing Petrov-Galerkin discretization of high-dimensional parametric PDEs , arXiv preprint arXiv:1701.01671, (2017)

    work page Pith review arXiv 2017

Show all 47 references
  1. [9]

    Chambolle and T

    A. Chambolle and T. Pock , A first-order primal-dual algorithm for convex problems with applications to imaging , Journal of mathematical imaging and vision, 40 (2011), pp. 120--145

    2011

  2. [10]

    Z. Chen, S. Zhong, J. Chen, and Y. Zhao , Deeppursuit: Uniting classical wisdom and deep rl for sparse recovery , in 2021 55th Asilomar conference on signals, systems, and computers, IEEE, 2021, pp. 1361--1366

    2021

  3. [11]

    C. Q. Choi , 7 revealing ways ais fail: Neural networks can be disastrously brittle, forgetful, and surprisingly bad at math , IEEE Spectrum, 58 (2021), pp. 42--47

    2021

  4. [12]

    M. J. Colbrook, V. Antun, and A. C. Hansen , The difficulty of computing stable and accurate neural networks: On the barriers of deep learning and smale’s 18th problem , Proceedings of the National Academy of Sciences, 119 (2022), p. e2107151119

    2022

  5. [13]

    Cuturi, O

    M. Cuturi, O. Teboul, and J.-P. Vert , Differentiable ranking and sorting using optimal transport , Advances in neural information processing systems, 32 (2019)

    2019

  6. [14]

    Dai and O

    W. Dai and O. Milenkovic , Subspace pursuit for compressive sensing signal reconstruction , IEEE transactions on Information Theory, 55 (2009), pp. 2230--2249

    2009

  7. [15]

    Daubechies, M

    I. Daubechies, M. Defrise, and C. De Mol , An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, 57 (2004), pp. 1413--1457

    2004

  8. [16]

    G. M. Davis, S. G. Mallat, and Z. Zhang , Adaptive time-frequency decompositions , Optical Engineering, 33 (1994), pp. 2183--2191

    1994

  9. [17]

    Fornasier and H

    M. Fornasier and H. Rauhut , Iterative thresholding algorithms , Applied and Computational Harmonic Analysis, 25 (2008), pp. 187--208

    2008

  10. [18]

    Foucart and H

    S. Foucart and H. Rauhut , A Mathematical Introduction to Compressive Sensing , Birkhäuser, New York, NY, 2013

    2013

  11. [19]

    M. P. Friedlander, H. Mansour, R. Saab, and \"O . Yilmaz , Recovering compressively sampled signals using partial support information , IEEE Transactions on Information Theory, 58 (2011), pp. 1122--1134

    2011

  12. [20]

    Gao and L

    B. Gao and L. Pavel , On the properties of the softmax function with application in game theory and reinforcement learning , arXiv preprint arXiv:1704.00805, (2017)

    2017 arXiv

  13. [21]

    Goodfellow, Y

    I. Goodfellow, Y. Bengio, A. Courville, and Y. Bengio , Deep learning , vol. 1, MIT press Cambridge, 2016

    2016

  14. [22]

    Gregor and Y

    K. Gregor and Y. LeCun , Learning fast approximations of sparse coding , in Proceedings of the 27th international conference on international conference on machine learning, 2010, pp. 399--406

    2010

  15. [23]

    Grover, E

    A. Grover, E. Wang, A. Zweig, and S. Ermon , Stochastic optimization of sorting networks via continuous relaxations , arXiv preprint arXiv:1903.08850, (2019)

    2019 arXiv

  16. [24]

    Heaven et al

    D. Heaven et al. , Why deep-learning ais are so easy to fool , Nature, 574 (2019), pp. 163--166

    2019

  17. [25]

    E. Jang, S. Gu, and B. Poole , Categorical reparameterization with gumbel-softmax , arXiv preprint arXiv:1611.01144, (2016)

    2016 arXiv

  18. [26]

    Jo , Iterative hard thresholding for weighted sparse approximation , arXiv preprint arXiv:1312.3582, (2013)

    J. Jo , Iterative hard thresholding for weighted sparse approximation , arXiv preprint arXiv:1312.3582, (2013)

    2013 arXiv

  19. [27]

    M. A. Khajehnejad, W. Xu, A. S. Avestimehr, and B. Hassibi , Analyzing weighted _1 minimization for sparse recovery with nonuniform sparse models , IEEE Transactions on Signal Processing, 59 (2011), pp. 1985--2001

    2011

  20. [28]

    Khatib, D

    R. Khatib, D. Simon, and M. Elad , Learned greedy method (lgm): A novel neural architecture for sparse coding and beyond , Journal of Visual Communication and Image Representation, 77 (2021), p. 103095

    2021

  21. [29]

    Kutyniok , The mathematics of reliable artificial intelligence , Collections, 57 (2024)

    G. Kutyniok , The mathematics of reliable artificial intelligence , Collections, 57 (2024)

    2024

  22. [30]

    G. Z. Li, D. Q. Wang, Z. K. Zhang, and Z. Y. Li , A weighted OMP algorithm for compressive UWB channel estimation , in Applied Mechanics and Materials, vol. 392, 2013, pp. 852--856

    2013

  23. [31]

    Liang, J

    D. Liang, J. Cheng, Z. Ke, and L. Ying , Deep magnetic resonance image reconstruction: Inverse problems meet neural networks , IEEE Signal Processing Magazine, 37 (2020), pp. 141--151

    2020

  24. [32]

    G. Mena, D. Belanger, S. Linderman, and J. Snoek , Learning latent permutations with gumbel-sinkhorn networks , arXiv preprint arXiv:1802.08665, (2018)

    2018 arXiv

  25. [33]

    Mohammad-Taheri and S

    S. Mohammad-Taheri and S. Brugiapaglia , The greedy side of the lasso: New algorithms for weighted sparse recovery via loss function-based orthogonal matching pursuit , Sampling Theory, Signal Processing, and Data Analysis, 23 (2025), p. 3

    2025

  26. [34]

    Mohammad-Taheri, M

    S. Mohammad-Taheri, M. J. Colbrook, and S. Brugiapaglia , OMP-Net : N eural network unrolling of weighted Orthogonal Matching Pursuit , in 2024 International Workshop on the Theory of Computational Sensing and its Applications to Radar, Multimodal Sensing and Imaging (CoSeRa),...

    2024

  27. [35]

    Monga, Y

    V. Monga, Y. Li, and Y. C. Eldar , Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing , IEEE Signal Processing Magazine, 38 (2021), pp. 18--44

    2021

  28. [36]

    Needell and J

    D. Needell and J. A. Tropp , CoSaMP : Iterative signal recovery from incomplete and inaccurate samples , Applied and Computational Harmonic Analysis, 26 (2009), pp. 301--321

    2009

  29. [37]

    Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad , Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition , in Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, IEEE, 1993, pp. 40--44

    1993

  30. [38]

    Prillo and J

    S. Prillo and J. Eisenschlos , Softsort: A continuous relaxation for the argsort operator , in International Conference on Machine Learning, PMLR, 2020, pp. 7793--7802

    2020

  31. [39]

    Rauhut and R

    H. Rauhut and R. Ward , Interpolation via weighted _1 minimization , Applied and Computational Harmonic Analysis, 40 (2016), pp. 321--351

    2016

  32. [40]

    M. E. Sander, J. Puigcerver, J. Djolonga, G. Peyr \'e , and M. Blondel , Fast, differentiable and sparse top-k: a convex analysis perspective , in International Conference on Machine Learning, PMLR, 2023, pp. 29919--29936

    2023

  33. [41]

    Scarlett, R

    J. Scarlett, R. Heckel, M. R. Rodrigues, P. Hand, and Y. C. Eldar , Theoretical perspectives on deep learning methods in inverse problems , IEEE journal on selected areas in information theory, 3 (2022), pp. 433--453

    2022

  34. [42]

    L. N. Trefethen and D. Bau , Numerical Linear Algebra , SIAM, 2022

    2022

  35. [43]

    Z. Wang, Q. Ling, and T. Huang , Learning deep ^0 encoders , in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 30, 2016

    2016

  36. [44]

    B. Xin, Y. Wang, W. Gao, D. Wipf, and B. Wang , Maximal sparsity with deep networks? , Advances in Neural Information Processing Systems, 29 (2016)

    2016

  37. [45]

    Zhang and B

    J. Zhang and B. Ghanem , Ista-net: Interpretable optimization-inspired deep network for image compressive sensing , in Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp. 1828--1837

    2018

  38. [46]

    Zhang , Sparse recovery with orthogonal matching pursuit under RIP , IEEE Transactions on Information Theory, 57 (2011), pp

    T. Zhang , Sparse recovery with orthogonal matching pursuit under RIP , IEEE Transactions on Information Theory, 57 (2011), pp. 6215--6221

    2011

  39. [47]

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