SLoG-Net: Algorithm Unrolling for Source Localization on Graphs

Chang Ye; Gonzalo Mateos

REVIEW 2 major objections 6 minor 46 references

SLoG-Net: Algorithm Unrolling for Source Localization on Graphs

T0 review · 2 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read By unrolling ADMM iterations, SLoG-Net turns blind source localization on graphs into a fast trainable network that matches the iterative solver's accuracy.

desk verdict A clean ADMM-unrolling paper with an honest comparison; just pin down the ADMM baseline's penalty parameters before accepting the 'on par' claim. read the letter →

arxiv 2501.00442 v1 pith:IYQDVLVZ submitted 2024-12-31 eess.SP

Chang Ye , Gonzalo Mateos This is my paper · ORCID

classification eess.SP

keywords graphsignalprocessingsourcelocalizationblinddeconvolutionalgorithmunrollingADMMfilterssparserecoverynetworkdiffusion

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

The paper claims that locating the source nodes of a network diffusion process, when the diffusion filter is unknown, reduces to a convex ℓ1-synthesis problem once the filter is invertible, and that unrolling the ADMM solver for that problem yields a neural network that matches the iterative baseline's accuracy while running orders of magnitude faster. The resulting model, SLoG-Net, learns step sizes, penalty parameters, thresholds, and the scale constraint from labeled data, removing the manual tuning that the ADMM baseline needs. The authors support the claim with experiments on synthetic random graphs, a community-detection comparison with a graph neural network, and a real-data study on Digg voting cascades.

What carries the argument

The argument is carried by the invertible-graph-filter assumption and the frequency-domain identity $\tilde{y} = \operatorname{diag}(\Psi_L h)\tilde{x}$. Under invertibility, the inverse filter $G=H^{-1}$ exists as a polynomial in the graph-shift operator, so $X=GY$ replaces the bilinear forward model with a linear one; the sparsity objective $\|X\|_{1,1}$ then factors as $\|(Y^\top V \odot V)\tilde{g}\|_1$, a convex linear program in the inverse filter's frequency response. ADMM solves this program with a filter update that inverts a rank-one correction of a diagonal matrix, a soft-thresholding source update, and dual multiplier updates; SLoG-Net unrolls these three steps into corresponding sub-layers with learnable combination weights, thresholds, penalty parameters, and constraint vectors $M$ and $m$, which is what lets the network be trained end-to-end from labeled data.

What would settle it

Take a graph and a filter $H$ whose frequency response is exactly zero at one graph eigenvalue, generate $Y=HX$ from sparse sources $X$, and run both the convex program (8) and a trained SLoG-Net on the observations; if either method still recovers the source support, then the invertibility assumption is not necessary as claimed, and if neither recovers it, the assumption is doing the load-bearing work.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that source localization on graphs can be solved through a convex program and that the ADMM iterations of that program can be truncated, parameterized, and trained without losing accuracy. With observations modeled as $Y=HX$ for a polynomial graph filter $H$, the invertibility of $H$ lets the authors rewrite the bilinear model as $X=GY$, where $G=H^{-1}$ is also a graph filter; estimating the inverse filter's frequency response $\tilde{g}$ then becomes the linear program $\min \|(Y^\top V \odot V)\tilde{g}\|_1$ subject to $1^\top \tilde{g} = 1$. The paper derives ADMM updates for this program, exploits the diagonal structure of $Z^\top Z$ to invert the needed matrix in $O(N^2)$ time, and unrolls the updates into a $K$-layer network with learnable parameters in each filter, sources, and multipliers sub-layer. The numerical results show SLoG-Net on par with ADMM on recovery error and support accuracy, with better noise robustness and inference times around $10^{-2}$ seconds compared with seconds for ADMM.

Load-bearing premise

The load-bearing premise is that the diffusion filter $H$ is invertible, meaning its frequency response is nonzero at every graph eigenvalue, so that the observations can be rewritten as $X=GY$ with $G=H^{-1}$ and the convex $\ell_1$ program applies.

Editorial extensions

If this is right

SLoG-Net matches the ADMM baseline on source recovery error and support accuracy while running roughly two to three orders of magnitude faster at inference, so model-based convex relaxations can be converted into deployable inference engines.
Because step sizes, penalty coefficients, thresholds, and the scale constraint are learned, users no longer need to hand-tune those quantities for each graph or noise level.
The architecture stays interpretable: each layer corresponds to an ADMM update, so behavior can be inspected and complexity can be controlled by choosing the number of layers $K$.
On the Digg 2009 data, SLoG-Net achieves a higher AUC than the IVGD baseline in identifying which users' early votes sparked a story's voting cascade, indicating the approach transfers beyond synthetic diffusion models.
The same ADMM blueprint applies to other blind graph deconvolution tasks that satisfy the invertibility condition, since the network is built from the solver updates rather than from task-specific features.

Reading between the lines

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

Because SLoG-Net is trained to imitate the convex relaxation (8), its performance ceiling is likely the convex program's recovery region; a testable extension is to train against the non-convex $\ell_0$ objective or filters outside the training distribution to see whether unrolling can surpass that baseline.
The architecture drops the common-support assumption of earlier lifted-matrix methods, so a natural next test is whether the layer-wise decoupled parameters transfer to larger graphs than those seen in training, which the paper lists as future work.
The invertibility assumption suggests an experimental design rule: choose diffusion dynamics whose frequency response stays bounded away from zero on the graph spectrum, because spectral nulls make both the convex program and its unrolled version blind to the lost modes.
The binary-data calibration trick, which chains an invertible residual network in front of SLoG-Net, indicates a broader pattern where unrolled graph-signal networks can be combined with learnable pre-processors whenever observations violate the diffusion model.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Read SLoG-Net. Bottom line: it does what it says. The ADMM derivation is clean, the unrolling is faithful, and the experiments back the accuracy claims. The main thing to fix before publication is the ADMM baseline: the penalty parameters are never specified, so the 'on par' claim is under-supported as reported.

What's new: this is the first ADMM unrolling for blind graph deconvolution on graphs, as far as the cited literature goes. The architectural refinements—learnable constraints M, m, decoupled per-layer parameters—are real changes, not a trivial transfer. They also give a standalone ADMM solver for the convex relaxation (8), which is useful in its own right. The matrix inversion lemma trick in Appendix C is correct and gives an O(N^2) inversion, and the paper shares code.

What's good: the derivations in Section III and Appendix A check out, the experiments are honest and cover noise, P, N, and several graph types with ten-run error bars. Limitations are disclosed: the invertibility assumption on H, small graph sizes, and the weak real-data AUC. None of these invalidates the stated claims.

The soft spot: the ADMM baseline's rho_lambda and rho_mu are not reported, and there's no grid search or sensitivity analysis. Those penalty parameters materially affect how fast ADMM converges and what solution it stops at. Since the paper's pitch is 'no manual tuning,' the comparison has to be against a reasonably tuned ADMM. As written, the timings and the 'on par' accuracy could be an artifact of a badly-tuned baseline. This is load-bearing but fixable: report the parameters, show a sensitivity sweep, and ideally include a tuned baseline.

Minor: the real-data AUC (0.56 vs 0.51) is weak and they say so; the synthetic graphs cap at 100 nodes, so scalability is modest. The invertibility assumption is a scope condition, not a hidden flaw.

Citation pattern is appropriate. Self-citation of [42] is justified because the convex relaxation is the foundation; the new result is the unrolling and the solver. No circularity.

Who it's for: GSP researchers, people working on algorithm unrolling, and anyone doing network inverse problems. It's a solid, honest paper and deserves a serious referee. I'd send it out and ask for the ADMM baseline details as a major revision item.

Referee Report

2 major / 6 minor

Summary. The paper studies blind deconvolution for source localization on graphs: given diffused graph signals Y generated from sparse sources X through an unknown graph filter H, it jointly estimates the inverse filter and the sources. Under an invertibility assumption on H, the authors reformulate the problem as a convex ℓ1-synthesis program, derive an ADMM solver, unroll the iterations into a trainable network called SLoG-Net, and evaluate the method on synthetic and real data. The central empirical claim is that SLoG-Net achieves accuracy on par with the iterative ADMM baseline while being orders of magnitude faster at inference and avoiding manual tuning of step-size or penalty parameters.

Significance. If the comparison is fair and the empirical claims hold, this is a useful contribution to the algorithm-unrolling literature for graph inverse problems. The paper gives a clean derivation of the ADMM updates, exploits the diagonal structure of Z^T Z and the matrix inversion lemma to make the model-based solver practical, and provides reproducible code for the experiments. The architecture is interpretable and parameter-efficient by construction, and the noise-robustness experiments show graceful degradation. The real-data experiment is honestly described as difficult, although the reported effect sizes are small.

major comments (2)

[Section V-B with Section III-B] The ADMM baseline is not fully specified in the numerical evaluation. The penalty parameters ρλ and ρμ, the stopping criterion, the maximum number of iterations, and the initialization are never reported, and it is not stated whether the experiments use the original constraint 1^T g = c or the modified constraint M^T g = m from Algorithm 1. Since the paper motivates SLoG-Net by the need to avoid manually tuning exactly these parameters, the comparison must demonstrate that ADMM was reasonably tuned; otherwise the 'on par' accuracy claim and the timing comparison in Table I could reflect an arbitrarily poor or slow baseline rather than a genuine property of the unrolled network. Please report the grid search or sensitivity analysis for ρλ and ρμ, the convergence criterion and iteration cap, and the exact ADMM variant used.
[Section V-E] The real-data experiment reports a mean AUC of 0.56 for SLoG-Net versus 0.51 for IVGD, which is close to chance, and no error bars, confidence intervals, or per-subgraph results are given. The sentence in Section V-E that SLoG-Net 'is better at learning representations that are predictive of the sources' is therefore stronger than the displayed evidence supports. Please provide the spread over the 10 realizations (and ideally a paired comparison), or temper the conclusion accordingly.

minor comments (6)

[Section IV-A and Fig. 2] Equation (16) defines the sources sub-layer with only α1 and α2, but the caption of Fig. 2 lists Θ_X^{(k)} = {α1, α2, α3, τ}. Please clarify what α3 is used for or remove it from the caption.
[Section V-A] The hyperparameter selection paragraph says that K = 5 and d = 2 were chosen after a grid search, but the grid values, the validation criterion, and the cost of the search are not given; please include these details to support the reproducibility claim.
[Fig. 2, Algorithm 1] The pseudocode in Fig. 2 uses notation such as ωω, ωµ, and ε^{-1}ω that does not match the ρλ, ρμ, and ρλ^{-1} used in Section III-B, and several occurrences of '↑' appear where a subtraction sign is intended; this makes the algorithm hard to read and should be corrected.
[Section V-B and Table I] The wall-clock timing comparisons do not report the hardware, software versions, or random seeds used; please add these details so that the claimed inference speedups can be reproduced and compared fairly.
[Entire text] There are several typos that should be corrected in revision, including 'syntethic' in Section IV-A, 'corruptin' in Section V-B, 'mangnitude' in Section V-B, 'pr thousands' in Section IV, and 'consisent' in Section V-A.
[Section IV-A and Section V-A] The text says initial states can be randomly initialized 'as we do in the ensuing experiments,' while Section III-B suggests zero initialization is typical; please state explicitly what initialization is used for the ADMM baseline and for SLoG-Net at both training and inference.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation found; the few self-citations are not load-bearing.

full rationale

The derivation chain is self-contained at the level that matters for the paper's claims. Section III-A starts from Assumption 2 (invertible H), writes X = GY, and derives the l1-synthesis program (8) via the identity ||GY||_{1,1} = ||(Y^T V circle V)\tilde g||_1; no step of this derivation uses the target result as an input. The ADMM updates (11)-(14) are obtained in Appendix A from the augmented Lagrangian (10), and SLoG-Net is formed by unrolling these updates with learnable parameters. Training minimizes a relative-error loss against ground-truth sources on a training set, and testing is carried out on independently generated (X_test, Y_test) pairs, so the reported RE and ACC numbers are not fitted quantities renamed as predictions. The ADMM baseline is a fixed iterative solver with its own penalty parameters; although the paper does not report how those baseline hyperparameters were tuned, that is a comparison-fairness concern, not circularity. The remaining self-citations ([42], [44]) provide recovery guarantees, identifiability remarks, and the overall problem formulation; however, the formulation is rederived in-paper, and the central empirical claim does not reduce to those citations. At most there is a minor non-load-bearing self-citation pattern, which the score of 2 reflects.

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

The central claim rests on standard GSP assumptions (known graph, sparse sources, invertible filter) plus the availability of labeled training data. No new physical entities are postulated. The learnable parameters of SLoG-Net are the main fitted quantities, and they are trained rather than derived.

free parameters (2)

SLoG-Net learnable weights Θ = learned via Adam on 200k training samples
Includes per-layer ρ1, ρ2, α1-α3, τ, β1-β3, γ, M, m; these are optimized to minimize the relative reconstruction error on the training set. They are not derived from first principles.
Hyperparameters K and d = K=5, d=2
Chosen via grid search on validation sets; they control network depth and the constraint subspace dimension.

assumptions (5)

domain assumption Assumption 1: sources X are sparse with at most S≪N nonzeros per column.
Section II-B. Needed to make the blind deconvolution problem identifiable and to justify the ℓ1 relaxation.
domain assumption Assumption 2: the graph filter H is invertible (frequency response nonzero at all graph eigenvalues).
Section III-A. Enables the linear reparameterization X=GY and the convex program (8); the entire method fails without it.
domain assumption The graph shift operator S is symmetric and its eigenbasis V is known.
Section II and V: all experiments use a known graph and the GFT basis. The method requires V to build Z=Y^T V ⊙ V.
domain assumption The diffusion forward model Y=HX holds exactly (or with additive noise) and filter order L is known.
Section II-B and V-A. Synthetic data is generated from this model; the method does not infer L.
domain assumption Training and test data are drawn from the same graph and source-filter distributions.
Section V: training and test use the same graph, same θ, and filter distribution; generalization to other graphs is future work.

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Pith. "Pith review of SLoG-Net: Algorithm Unrolling for Source Localization on Graphs." pith.science (2026). https://pith.science/paper/IYQDVLVZ

@misc{pith2026250100442,
  author       = {Pith},
  title        = {Pith review of: SLoG-Net: Algorithm Unrolling for Source Localization on Graphs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IYQDVLVZ}},
  note         = {Machine review of arXiv:2501.00442}
}

read the original abstract

We present a novel model-based deep learning solution for the inverse problem of localizing sources of network diffusion. Starting from first graph signal processing (GSP) principles, we show that the problem reduces to joint (blind) estimation of the forward diffusion filter and a sparse input signal that encodes the source locations. Despite the bilinear nature of the observations in said blind deconvolution task, by requiring invertibility of the diffusion filter we are able to formulate a convex optimization problem and solve it using the alternating-direction method of multipliers (ADMM). We then unroll and truncate the novel ADMM iterations to arrive at a parameterized neural network architecture for Source Localization on Graphs (SLoG-Net), that we train in an end-to-end fashion using labeled data. This supervised learning approach offers several advantages such as interpretability, parameter efficiency, and controllable complexity during inference. Our reproducible numerical experiments corroborate that SLoG-Net exhibits performance on par with the iterative ADMM baseline, but with markedly faster inference times and without needing to manually tune step-size or penalty parameters. Overall, our approach combines the best of both worlds by incorporating the inductive biases of a GSP model-based solution within a data-driven, trainable deep learning architecture for blind deconvolution of graph signals.

Figures

Figures reproduced from arXiv: 2501.00442 by the authors.

**Figure 2.** The layerwise structure of SLoG-Net, a DL model [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Recovery performance vs. training set size [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Recovery performance of SLoG-Net vs. ADMM for different noise [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: A visual comparison of SLoG-Net and ADMM for a representative [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Recovery performance of SLoG-Net vs. ADMM for different number ˆ [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 8.** Figure 8: (top) Pre-training architecture and (bottom) calibrated SLoG-Net. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: The ROC curve of SLoG-Net vs. IVGD for one representative sampled [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

46 extracted references · 38 canonical work pages

[42]

Blind deconvolution on graphs: Exact and stable recovery,

——, “Blind deconvolution on graphs: Exact and stable recovery,” Signal Process., vol. 230, p. 109864, May 2025

work page 2025
[1]

Blind deconvolution using convex programming,

A. Ahmed, B. Recht, and J. Romberg, “Blind deconvolution using convex programming,”IEEE Trans. Inf. Theory, vol. 60, no. 3, pp. 1711– 1732, 2014

work page 2014
[2]

A fast iterative shrinkage-thresholding algorithm for linear inverse problems,

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. , vol. 2, no. 1, pp. 183–202, 2009

2009
[3]

Invertible residual networks,

J. Behrmann, W. Grathwohl, R. T. Chen, D. Duvenaud, and J.-H. Jacobsen, “Invertible residual networks,” in Proc. Int. Conf. Mach. Learn., 2019, pp. 573–582

work page 2019
[4]

D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computa- tion: Numerical Methods , 2nd ed. Athena-Scientific, 1999

work page 1999
[5]

Distributed optimization and statistical learning via the alternating direction method of multipliers,

S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al., “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations and Trends® in Machine learning , vol. 3, no. 1, pp. 1–122, 2011

2011
[6]

Graph unrolling networks: Inter- pretable neural networks for graph signal denoising,

S. Chen, Y . C. Eldar, and L. Zhao, “Graph unrolling networks: Inter- pretable neural networks for graph signal denoising,” IEEE Trans. Signal Process., vol. 69, pp. 3699–3713, 2021

work page 2021
[7]

Reaching a consensus,

M. H. DeGroot, “Reaching a consensus,” J. Am. Stat. Assoc , vol. 69, pp. 118–121, 1974

work page 1974

Show all 46 references

[8]

Network infusion to infer information sources in networks,

S. Feizi, M. M ´edard, G. Quon, M. Kellis, and K. Duffy, “Network infusion to infer information sources in networks,” IEEE Trans. Netw. Sci. Eng., vol. 6, no. 3, pp. 402–417, 2018

2018
[9]

Graphs, convolutions, and neural networks: From graph filters to graph neural networks,

F. Gama, E. Isufi, G. Leus, and A. Ribeiro, “Graphs, convolutions, and neural networks: From graph filters to graph neural networks,” IEEE Signal Process. Mag. , vol. 37, no. 6, pp. 128–138, 2020

2020
[10]

Convolutional neural network architectures for signals supported on graphs,

F. Gama, A. G. Marques, G. Leus, and A. Ribeiro, “Convolutional neural network architectures for signals supported on graphs,” IEEE Trans. Signal Process., vol. 67, no. 4, pp. 1034–1049, 2019

2019
[11]

On the shift operator, graph frequency, and optimal filtering in graph signal processing,

A. Gavili and X.-P. Zhang, “On the shift operator, graph frequency, and optimal filtering in graph signal processing,” IEEE Trans. Signal Process., vol. 65, no. 23, pp. 6303–6318, 2017

2017
[12]

Decentralized learning for wireless communications and networking,

G. B. Giannakis, Q. Ling, G. Mateos, I. D. Schizas, and H. Zhu, “Decentralized learning for wireless communications and networking,” in Splitting Methods in Communication, Imaging, Science, and Engi- neering, R. Glowinski, S. J. Osher, and W. Yin, Eds. Springer, 2016, pp. 461–497

2016
[13]

Learning fast approximations of sparse coding,

K. Gregor and Y . LeCun, “Learning fast approximations of sparse coding,” in Proc. Int. Conf. Mach. Learn. , 2010, p. 399–406

2010
[14]

Social dynamics of Digg,

T. Hogg and K. Lerman, “Social dynamics of Digg,” EPJ Data Sci. , vol. 1, pp. 1–26, 2012

2012
[15]

R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge University Press, 2013

2013
[16]

Localizing sources of brain disease progression with network diffusion model,

C. Hu, X. Hua, J. Ying, P. M. Thompson, G. E. Fakhri, and Q. Li, “Localizing sources of brain disease progression with network diffusion model,” IEEE J. Sel. Topics Signal Process. , vol. 10, no. 7, pp. 1214– 1225, 2016

2016
[17]

Graph filters for signal processing and machine learning on graphs,

E. Isufi, F. Gama, D. I. Shuman, and S. Segarra, “Graph filters for signal processing and machine learning on graphs,” IEEE Trans. Signal Process., pp. 1–32, 2024

2024
[18]

Adam: A method for stochastic optimization,

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” in Proc. Int. Conf. Learn. Representations , 2015, pp. 1–15

2015
[19]

Understanding blind deconvolution algorithms,

A. Levin, Y . Weiss, F. Durand, and W. T. Freeman, “Understanding blind deconvolution algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 33, no. 12, pp. 2354–2367, 2011

2011
[20]

Identifiability in bilinear inverse problems with applications to subspace or sparsity-constrained blind gain and phase calibration,

Y . Li, K. Lee, and Y . Bresler, “Identifiability in bilinear inverse problems with applications to subspace or sparsity-constrained blind gain and phase calibration,” IEEE Trans. Inf. Theory , vol. 63, no. 2, pp. 822– 842, Feb 2017

2017
[21]

Self-calibration and biconvex compressive sensing,

S. Ling and T. Strohmer, “Self-calibration and biconvex compressive sensing,” Inverse Probl., vol. 31, no. 115002, pp. 1–31, 2015

2015
[22]

In-network sparsity- regularized rank minimization: Algorithms and applications,

M. Mardani, G. Mateos, and G. B. Giannakis, “In-network sparsity- regularized rank minimization: Algorithms and applications,” IEEE Trans. Signal Process. , Mar. 2012 (submitted; see also arXiv preprint arXiv:1203.1570 [cs.MA])

2012 arXiv
[23]

Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing,

V . Monga, Y . Li, and Y . C. Eldar, “Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing,” IEEE Signal Process. Mag., vol. 38, no. 2, pp. 18–44, 2021

2021
[24]

Graph signal restoration using nested deep algorithm unrolling,

M. Nagahama, K. Yamada, Y . Tanaka, S. H. Chan, and Y . C. Eldar, “Graph signal restoration using nested deep algorithm unrolling,” IEEE Trans. Signal Process., vol. 70, pp. 3296–3311, 2022

2022
[25]

Graph signal processing: Overview, challenges, and ap- plications,

A. Ortega, P. Frossard, J. Kova ˇcevi´c, J. M. F. Moura, and P. Van- dergheynst, “Graph signal processing: Overview, challenges, and ap- plications,” Proc. IEEE, vol. 106, no. 5, pp. 808–828, 2018

2018
[26]

Source localization on graphs via ℓ1 recovery and spectral graph theory,

R. Pena, X. Bresson, and P. Vandergheynst, “Source localization on graphs via ℓ1 recovery and spectral graph theory,” in Proc. IEEE Image, Video, and Multidimens. Signal Process. Workshop , 2016, pp. 1–5

2016
[27]

Locating the source of diffusion in large-scale networks,

P. C. Pinto, P. Thiran, and M. Vetterli, “Locating the source of diffusion in large-scale networks,” Phys. Rev. Lett., vol. 109, no. 068702, pp. 1–5, 2012

2012
[28]

Learning to learn graph topologies,

X. Pu, T. Cao, X. Zhang, X. Dong, and S. Chen, “Learning to learn graph topologies,” in Proc. Adv. Neural. Inf. Process. Syst. , 2021, pp. 1–14

2021
[29]

Graph-signal reconstruc- tion and blind deconvolution for structured inputs,

D. Ram ´ırez, A. G. Marques, and S. Segarra, “Graph-signal reconstruc- tion and blind deconvolution for structured inputs,” Signal Processing, vol. 188, p. 108180, 2021

2021
[30]

Discrete signal processing on graphs: Frequency analysis,

A. Sandryhaila and J. M. F. Moura, “Discrete signal processing on graphs: Frequency analysis,” IEEE Trans. Signal Process. , vol. 62, no. 12, pp. 3042–3054, June 2014

2014
[31]

Discrete signal processing on graphs,

A. Sandryhaila and J. M. Moura, “Discrete signal processing on graphs,” IEEE Trans. Signal Process. , vol. 61, no. 7, pp. 1644–1656, 2013

2013
[32]

Diffusion archeology for diffusion progres- sion history reconstruction,

E. Sefer and C. Kingsford, “Diffusion archeology for diffusion progres- sion history reconstruction,” in Proc. IEEE Conf. on Data Mining, 2014, pp. 530–539

2014
[33]

Blind identifi- cation of graph filters,

S. Segarra, G. Mateos, A. G. Marques, and A. Ribeiro, “Blind identifi- cation of graph filters,” IEEE Trans. Signal Process., vol. 65, no. 5, pp. 1146–1159, 2017

2017
[34]

GLAD: Learning sparse graph recovery,

H. Shrivastava, X. Chen, B. Chen, G. Lan, S. Aluru, and L. Song, “GLAD: Learning sparse graph recovery,” in Proc. Int. Conf. Learn. Representations, 2020, pp. 1–22

2020
[35]

Blind deconvolution of sparse graph signals in the presence of perturbations,

V . M. Tenorio, S. Rey, and A. G. Marques, “Blind deconvolution of sparse graph signals in the presence of perturbations,” in Proc. Int. Conf. Acoustics, Speech, Signal Process. , 2024, pp. 9406–9410

2024
[36]

An invertible graph diffusion neural network for source localization,

J. Wang, J. Jiang, and L. Zhao, “An invertible graph diffusion neural network for source localization,” in Proc. ACM Web Conf. , 2022, pp. 1058–1069

2022
[37]

Blind deconvolution from multiple sparse inputs,

L. Wang and Y . Chi, “Blind deconvolution from multiple sparse inputs,” IEEE Signal Process. Lett. , vol. 23, no. 10, pp. 1384–1388, 2016

2016
[38]

Graph structure learning with inter- pretable Bayesian neural networks,

M. Wasserman and G. Mateos, “Graph structure learning with inter- pretable Bayesian neural networks,” Trans. Mach. Learn. Res., pp. 1–27, 2024

2024
[39]

Learning graph structure from convolutional mixtures,

M. Wasserman, S. Sihag, G. Mateos, and A. Ribeiro, “Learning graph structure from convolutional mixtures,” Trans. Mach. Learn. Res. , pp. 1–29, 2023

2023
[40]

ADMM-CSNet: A deep learning approach for image compressive sensing,

Y . Yang, J. Sun, H. Li, and Z. Xu, “ADMM-CSNet: A deep learning approach for image compressive sensing,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 42, no. 3, pp. 521–538, 2020

2020
[41]

Blind deconvolution of graph signals: Robustness to graph perturbations,

C. Ye and G. Mateos, “Blind deconvolution of graph signals: Robustness to graph perturbations,” IEEE Signal Process. Lett. , Dec. 2024 (submit- ted; see also arXiv preprint arXiv:2412.15133 [eess.SP])

2024 arXiv
[43]

Learning to identify sources of network diffusion,

——, “Learning to identify sources of network diffusion,” in Proc. of European Signal Process. Conf. , 2022, pp. 727–731

2022
[44]

Blind identification of invertible graph filters with multiple sparse inputs,

C. Ye, R. Shafipour, and G. Mateos, “Blind identification of invertible graph filters with multiple sparse inputs,” in Proc. of European Signal Process. Conf., 2018, pp. 121–125

2018
[45]

One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations,

H. Zhang, M. Yan, and W. Yin, “One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations,” Adv. Comput. Math., vol. 42, no. 6, pp. 1381–1399, 2016

2016
[46]

Towards anomalous diffusion sources detection in a large network,

P. Zhang, J. He, G. Long, G. Huang, and C. Zhang, “Towards anomalous diffusion sources detection in a large network,” ACM T. Internet Techn., vol. 16, no. 1, pp. 1–24, 2016

2016

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [42]

Blind deconvolution on graphs: Exact and stable recovery,

——, “Blind deconvolution on graphs: Exact and stable recovery,” Signal Process., vol. 230, p. 109864, May 2025

work page 2025

[2] [1]

Blind deconvolution using convex programming,

A. Ahmed, B. Recht, and J. Romberg, “Blind deconvolution using convex programming,”IEEE Trans. Inf. Theory, vol. 60, no. 3, pp. 1711– 1732, 2014

work page 2014

[3] [2]

A fast iterative shrinkage-thresholding algorithm for linear inverse problems,

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. , vol. 2, no. 1, pp. 183–202, 2009

2009

[4] [3]

Invertible residual networks,

J. Behrmann, W. Grathwohl, R. T. Chen, D. Duvenaud, and J.-H. Jacobsen, “Invertible residual networks,” in Proc. Int. Conf. Mach. Learn., 2019, pp. 573–582

work page 2019

[5] [4]

D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computa- tion: Numerical Methods , 2nd ed. Athena-Scientific, 1999

work page 1999

[6] [5]

Distributed optimization and statistical learning via the alternating direction method of multipliers,

S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al., “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations and Trends® in Machine learning , vol. 3, no. 1, pp. 1–122, 2011

2011

[7] [6]

Graph unrolling networks: Inter- pretable neural networks for graph signal denoising,

S. Chen, Y . C. Eldar, and L. Zhao, “Graph unrolling networks: Inter- pretable neural networks for graph signal denoising,” IEEE Trans. Signal Process., vol. 69, pp. 3699–3713, 2021

work page 2021

[8] [7]

Reaching a consensus,

M. H. DeGroot, “Reaching a consensus,” J. Am. Stat. Assoc , vol. 69, pp. 118–121, 1974

work page 1974