Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling

Gabriele D'Acunto; Leonardo Di Nino; Paolo Di Lorenzo; Sergio Barbarossa

REVIEW 3 major objections 4 minor 43 references

Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A network sheaf — vector spaces on nodes and edges linked by linear maps — carries a full signal-processing toolkit for heterogeneous data.

desk verdict A coherent sheaf-SP toolkit with a genuinely useful representation-sheaf idea, but the headline spectral-fidelity guarantee rests on a restrictive factorization assumption that the experiments either construct or sidestep. read the letter →

arxiv 2608.01318 v1 pith:YBCC6ICF submitted 2026-08-02 eess.SP cs.AIcs.LG

Gabriele D'Acunto , Leonardo Di Nino , Paolo Di Lorenzo , Sergio Barbarossa This is my paper · ORCID

classification eess.SPcs.AIcs.LG MSC 05C5055N3094A12

keywords networksheavessheafsignalprocessingLaplacianFouriertransformheterogeneoussignalsgraphsamplingandrecoverynaturaltransformations

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

Network sheaves place a vector space on every node and edge of a graph, with linear maps tying neighboring spaces together; this paper tries to prove that this structure is enough to rebuild the whole signal-processing toolkit—spectral analysis, filtering, and sampling—for signals that live in different dimensions, units, or modalities on one network. The authors define a Sheaf Fourier Transform from the sheaf Laplacian, whose frequencies are not just graph-topological but jointly encode topology, the linear transport maps, and local geometry. Their key structural claim is an intertwining identity: when the raw signal sheaf is related to a lower-dimensional representation sheaf through a natural transformation, filtering and spectral analysis can be run in the small representation space and then lifted back without loss. If correct, the framework would give heterogeneous network data a single principled language for smoothness, filtering, and sample recovery, and it would collapse to classical graph signal processing when all stalks are one-dimensional and all restriction maps are identities.

What carries the argument

The central object is a network sheaf: Hilbert-space stalks on nodes and edges plus linear restriction maps $F_{i\trianglelefteq e}$, with the sheaf Laplacian $L_F = B^*B$ measuring the total inconsistency of a node signal. The argument runs on the pair (signal sheaf $F$, representation sheaf $J$) connected by a natural transformation $\delta$—a family of linear maps, assembled into a block-diagonal node operator $D_0$, that commutes with all restriction maps. The identity that carries the argument is the intertwining relation $L_F D_0 = D_0 L_J$, proved under the metric-compatible lift assumption on the restriction maps. This one identity makes the representation sheaf spectrally faithful: it maps every eigenspace of $L_J$ into an eigenspace of $L_F$ with the same frequency, makes polynomial filters commute with the lift ($h(L_F)D_0 = D_0 h(L_J)$), and produces the band splitting $B_K = \mathrm{Im}(B^\parallel_K) \oplus \mathrm{Im}(B^\perp_K)$ that drives the sampling savings.

What would settle it

Compute $L_F D_0 - D_0 L_J$ on a network sheaf with random restriction maps and independently chosen dictionaries, so Eq. (26) is violated. Under the paper's claimed necessary condition, the difference is nonzero, the spectra of the two sheaves do not correspond, and a signal with dictionary-orthogonal energy is not recoverable from the reduced sample budget. The same computation on a sheaf built to satisfy Eq. (26) should give a zero difference and exact recovery, separating the load-bearing lift condition from the rest of the framework.

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Extended reading notes

Core claim

The paper's central claim is that a network sheaf carries a complete classical signal-processing stack. The Sheaf Fourier Transform is the generalized eigendecomposition of the sheaf Laplacian $L_J$; the frequency $\lambda$ of a mode $u$ is its total inconsistency, $\lambda = \mathrm{TV}(u) = \sum_e \|J_{i\trianglelefteq e}u_i - J_{j\trianglelefteq e}u_j\|^2_{H_e}$. The structural result that makes the toolkit work is the intertwining $L_F D_0 = D_0 L_J$ between the signal sheaf Laplacian $L_F$ and the representation sheaf Laplacian $L_J$, obtained when the signal sheaf's restriction maps are the metric-compatible lifts $F_{i\trianglelefteq e} = D_e J_{i\trianglelefteq e} H_i^{-1} D_i^T G_i$. This identity implies a one-to-one spectral correspondence between eigenspaces, makes polynomial sheaf filters commute with lifting, and induces an orthogonal splitting of every band into a model-aligned component and a model-orthogonal component. On the sampling side, perfect recovery of a bandlimited sheaf signal from samples $\Psi_S x$ is characterized by $\mathrm{rank}(\Psi_S V_K) = b_K$, and the $\delta$-informed splitting lets the required sample count drop from the full bandwidth $b_K$ to the dimension of the model-aligned part. Experiments on synthetic signals, motion-capture data, and financial portfolios show the resulting filters and samplers outperforming graph-signal baselines.

Load-bearing premise

The whole chain assumes that the raw-data maps are built from the low-dimensional dictionaries by one specific formula (Eq. 26); if a given dataset's sheaf does not satisfy that formula, the spectral correspondence, filter commutation, and sampling savings are not guaranteed.

Editorial extensions

If this is right

A single spectral object, the sheaf Laplacian, supplies a variational notion of smoothness for heterogeneous signals, so methods built on the graph Fourier transform—spectral clustering, denoising, compression—can be lifted to multimodal network data.
Because every polynomial filter satisfies $h(L_F)D_0 = D_0 h(L_J)$, signal processing can be designed and executed in the low-dimensional representation space; the computational cost is governed by the representation stalk dimension, not the raw-signal dimension.
Sampling becomes a joint choice of nodes and intra-stalk entries; a bandlimited sheaf signal is perfectly recoverable exactly when $\mathrm{rank}(\Psi_S V_K)=b_K$, and the minimum number of samples equals the bandwidth.
For signals that live in the dictionary subspace, the band-splitting result reduces the required samples to the dimension of the model-aligned component, a saving that can be much smaller than the nominal bandwidth when the raw Laplacian has large degenerate eigenspaces.
The framework contains graph signal processing as the special case of scalar stalks with identity restriction maps, so existing graph-signal results are unified rather than discarded.

Reading between the lines

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

One extension the paper leaves implicit is to turn the lift condition into a design loss: fit dictionaries so that the residual $L_F D_0 - D_0 L_J$ is small, which would extend the framework to data-driven sheaf estimation.
Because the intrinsic spectral representation uses eigenspace projectors rather than individual eigenvectors, a natural next step is to feed those projectors into sheaf-based learning methods, making them invariant to basis choice inside degenerate eigenspaces.
A testable consequence is that the framework under-samples any real signal component the local dictionaries cannot represent; this predicts that good dictionaries must capture exactly the components that carry the task-relevant part of the signal.

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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

Colleague—

Bottom line: this is a serious, mostly well-built paper that delivers a coherent sheaf-theoretic SP toolkit, but the headline guarantee—that the low-dimensional representation sheaf is spectrally faithful—is conditional on a strong factorization assumption (Eq. 26) that the experiments either construct or explicitly abandon. The paper deserves a careful referee, but it needs a major revision to delimit where the theory actually applies.

What is genuinely new: the representation sheaf construction via natural transformations. Props. III.1–III.3 give clean local conditions for when dictionaries induce a consistent lower-dimensional sheaf, and Prop. III.3 ties global sections across the two sheaves. The SFT and the emphasis on basis-invariant eigenspaces rather than individual eigenvectors is a sensible handling of spectral multiplicity. And the δ-informed band splitting in Cor. VI.3 is a real idea: if you know the signal lies in the dictionary span, you can recover with fewer samples than the full bandwidth. The motion-capture experiment is a thoughtful, physically motivated sheaf construction, not a toy.

The soft spot is exactly where the stress-test note points. Thm. IV.1 requires Eq. (26), which forces each restriction map to factor through the dictionary subspace and annihilate the orthogonal complement. That is a rank-deficient structural assumption; nothing in the definition of a signal sheaf gives it to you. The paper presents no necessary-and-sufficient condition for an arbitrary sheaf to admit a spectrally faithful representation, only a sufficient one. The experiments confirm the worry: Sec. VII-A builds F from latent factors and defines J afterward, and the text admits the intertwining does not hold there; Sec. VII-B (motion capture) never mentions Eq. (26), so the spectral guarantees don't apply; Sec. VII-C constructs F via Eq. (26) and generates test signals from the same J, making it a self-consistency check. Showing that L_J still beats L_F in Sec. VII-A is interesting evidence that the representation sheaf can be useful beyond the theorem, but it doesn't repair the theory gap.

Also worth tightening: the 'first unified SSP framework' claim sits oddly next to Robinson's earlier sheaf-theoretic work on sampling and filtering; the precise difference should be stated more sharply.

Who is this for? People working on GSP/TSP who need a common language for heterogeneous stalk-valued signals. It will be cited, and a serious referee should read it. But in current form the central theorem's domain is narrower than the title suggests.

Referee Report

3 major / 4 minor

Summary. The paper proposes a unified sheaf-theoretic signal processing (SSP) framework for heterogeneous network signals, extending graph signal processing (GSP) and topological signal processing (TSP) to settings where node and edge stalks have different dimensions, units, and geometries. The authors define the Sheaf Fourier Transform (SFT) from the eigendecomposition of the sheaf Laplacian, introduce polynomial sheaf filters, and formulate sampling as joint selection of nodes and intra-stalk coordinates, with perfect recovery characterized by a rank condition. A key structural contribution is the construction of a lower-dimensional "representation sheaf" J related to the raw "signal sheaf" F via a natural transformation δ, and the proof of the spectral intertwining L_F D_0 = D_0 L_J under the metric-compatible lift condition (Eq. 26). This intertwining underpins the spectral correspondence, filter commutation, and a δ-driven band splitting that reduces the sampling burden. Experiments on synthetic data, the CMU Panoptic motion-capture dataset, and a financial portfolio dataset compare the proposed framework against GSP baselines.

Significance. If the central claims are accepted, the paper provides a coherent and genuinely general language for spectral analysis, filtering, and sampling of stalk-valued signals, going beyond fixed-dimension GSP/TSP. The supplement contains complete proofs and the algebraic core is internally consistent under the stated assumptions. The eigenspace-level treatment of spectral multiplicity in Sec. IV-C is a clean and useful contribution, and the explicit recognition that the intertwining can fail for physically motivated sheaves (Sec. VII-A) is honest. However, the broad claims of a "unified SSP framework" and of guaranteed spectral fidelity and δ-driven sampling savings are only proven under the strong condition (Eq. 26), and the empirical sections do not validate the theory outside that condition. The paper therefore has a sound mathematical core but currently overstates its applicability, which is a load-bearing scope issue rather than a purely presentational one.

major comments (3)

[IV-B, Eq. (26)] Theorem IV.1 and all downstream results (Cor. IV.2, Cor. V.1, Cor. VI.3) are proven only under the metric-compatible lift condition F_{i⊴e}=D_e J_{i⊴e} H_i^{-1} D_i^T G_i. This is a strong structural constraint: it forces F to act only through the dictionary subspace and to annihilate the dictionary-orthogonal part of every raw signal. The paper provides no necessary-and-sufficient characterization of when an arbitrary signal sheaf admits such a spectrally faithful representation, and no perturbation bound for the error in the intertwining when Eq. (26) is violated. The general claims of spectral fidelity and of reduced-dimension processing with no loss of information are therefore not supported for general network sheaves. Please either explicitly state the framework as conditional on Eq. (26), or add a characterization/robustness analysis that quantifies the deviation from the intertwining when Eq. (26) fails.
[Sec. VII-A] This experiment compares filtering with L_J and L_F in a setting where the authors themselves state that the spectral intertwining of Thm. IV.1 "does not hold here": the restriction maps of F are built from physical latent factors and J is defined afterward. The reported superiority of L_J over the baselines therefore does not validate the spectral-correspondence machinery; it only shows that a hand-designed representation sheaf can be a better filter domain than the raw signal sheaf in this particular construction. To support the central claim, the experiment should include a configuration where Eq. (26) holds by construction (or report a quantitative measure of the violation and its effect on filter commutation). Without this, the empirical section does not provide evidence for the load-bearing theoretical result.
[Sec. VII-C] The financial sampling experiment constructs F exactly via Eq. (26) and generates bandlimited test signals from the eigenspaces of the same representation sheaf J (Eq. (62)). The striking savings of 9 raw samples versus 182 for the δ-agnostic approach is therefore an in-sample consistency check: the target recovery subspace is by construction the same subspace from which the signals are drawn. The δ-agnostic baseline requiring b=182 samples is also an expected artifact of the 178-dimensional kernel of L_F and the arbitrary eigenbasis inside that degenerate eigenspace. To support a practical advantage of the δ-driven sampling savings, please add an out-of-sample evaluation (e.g., signals not synthesized from the eigenspaces of the same J, or a leave-one-out style protocol) and report how the savings degrade when Eq. (26) is only approximately satisfied.

minor comments (4)

[Sec. VII-A] The word "addiditve" in the description of the noise should be "additive".
[VI-A, after Cor. VI.2] The phrase "It is worth to point out" is awkward; please use "It is worth pointing out".
[Sec. III, before Eq. (11)] The edge representation dimension c_e is used in Prop. III.1 but is not defined in the text preceding it; please define c_e explicitly together with D_e and H_e.
[Sec. IV-C] The definition of the eigenspace projector P_k in Eq. (31) assumes an H0-orthonormal basis U_k; this is correct, but it would help to state explicitly that P_k is independent of the basis choice because the H0-orthonormal frame is unique up to orthogonal transformations within the eigenspace.

Circularity Check

1 steps flagged · score 4.0 of 10

The core theorems are conditional and proven rather than circular, but the financial experiment closes the validation loop: F is defined from J via Eq. (26) and test signals are generated from the same representation eigenspaces, so the exact recovery is an in-sample consistency check.

fitted input called prediction [Sec. VII-C, around Eq. (26) and Eq. (62); Cor. IV.2]
"The restriction maps of F are obtained by lifting the representation-level restriction through the dictionaries via Eq. (26) (metric tensors here are the identity), thus guaranteeing exact spectral correspondence. ... A bandlimited test signal is then generated on J following the eigenspace-uniform procedure of Eq. (62) ... By Cor. IV.2, lifting the generated representation to the signal sheaf F via the dictionaries yields a signal x with the same energy as s on the same Ksig eigenspaces."

In the financial experiment the signal sheaf F is defined as the metric-compatible lift of J through Eq. (26), so the spectral correspondence of Cor. IV.2 holds by construction. The test signal is synthesized from eigenspaces of L_J and lifted to F, so it lies, by construction, in the δ-aligned subspace D_0 U_K used for recovery. Exact reconstruction with b=9 samples is therefore a theorem-consistency check rather than an out-of-sample prediction. The dictionaries D_i are also fitted from the same stock-return time series that defines the model, further closing the loop. The theorem itself is not circular, but this experiment does not independently test the key assumption Eq. (26).

full rationale

The mathematical derivation chain is largely self-contained: the SFT is defined from the sheaf Laplacian, Thm. IV.1 states the intertwining under the explicit structural assumption Eq. (26) and gives a proof, Cor. IV.2 and Cor. V.1 are direct consequences, and Thm. VI.1 is a linear-algebra sampling identity with a proof. The assumption Eq. (26) is transparent and the paper openly notes when it fails (Sec. VII-A: 'the spectral intertwining of Thm. IV.1 does not hold here: the restriction maps of F are not derived from J, but the converse'), which is an honest limitation rather than a circular dodge. Self-citations such as [5] for graph sampling are standard external mathematical results and are not load-bearing in a circular way; Supp. S3's citation of the authors' own [44] only illustrates spectral multiplicity and does not carry the main argument. The main caveat is the empirical validation: the synthetic filtering experiment generates signals from the eigenspaces of L_J used for filtering, and the financial experiment constructs F from J via Eq. (26) and generates test signals from J, so the reported exact recovery is an in-sample consistency check. This closes the validation loop and warrants a moderate score, but it does not reduce the central theorems to their inputs.

Assumptions & free parameters 4 free parameters · 6 assumptions · 2 invented entities

The central theorems have no numerical free parameters, but the framework's applicability rests on strong modeling choices: dictionaries, the lift condition, and bandlimitedness. These are explicit but not independently validated, which is why the ledger is not empty.

free parameters (4)

Representation dimension c_i = c=10 in Sec. VII-A; c=5 in Sec. VII-C
Hand-selected dimensionality of representation sheaf stalks; determines the low-dimensional subspace and the sampling budget. Not derived from first principles.
Synthetic correlation C=C1=C2 = Not stated in text
Controls factor correlation in the synthetic filtering experiment; the value is not given, so the experiment is not fully reproducible as written.
Optimal spectral bandwidth = Chosen per SNR by exploring the NMSE trade-off
Filtering results report the optimal relative bandwidth rather than a validation-selected value, which can favor the proposed method.
Dictionaries D_i = DCT in Sec. VII-A; five PCA/statistical factors in Sec. VII-C
Data-driven inputs. In the finance experiment, dictionaries are estimated from the same return series used to define the signal model, so part of the representation is learned from the test data.

assumptions (6)

standard math Finite-dimensional real Hilbert space linear algebra with metric tensors
Used throughout for adjoints, orthogonal projectors, and eigendecompositions; standard background collected in Supp. S1.
standard math Network sheaf axioms and natural transformations from category theory
Defines stalks, restriction maps, coboundary, and global sections; cites Mac Lane and Curry for foundational definitions.
domain assumption Signal sheaf F is given or constructed a priori
Sec. III states that F is assumed known and data-driven estimation is future work; this limits the practical scope of the framework.
ad hoc to paper Metric-compatible lift condition of Eq. (26)
Required for the intertwining theorem; assumes signal-sheaf restriction maps factor through the representation dictionaries and annihilate dictionary-orthogonal components. Not verified for general signal sheaves.
domain assumption Bandlimited signal model relative to the sheaf Laplacian
The sampling theorem applies only to signals in a finite-dimensional eigenspace subspace; this is a standard GSP assumption but strong in practice.
domain assumption Dictionaries belong to the Stiefel manifold
Eq. (8) assumes D_i^T D_i = I; non-orthonormal dictionaries would require a modified construction of metrics and restriction maps.

invented entities (2)

Representation sheaf J
purpose: Low-dimensional computational and representational domain for spectral filtering and sampling, linked to the signal sheaf by a natural transformation.
A formal construction defined by the authors; it has internal mathematical support from the theorems but no independent external or falsifiable handle.
Sheaf Fourier modes and sheaf frequencies
purpose: Eigenvectors and eigenvalues of the sheaf Laplacian used to define the Sheaf Fourier Transform and filters.
Defined in Sec. IV-A as the sheaf analogue of graph Fourier modes; they are definitional and carry no external prediction.

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Pith. "Pith review of Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling." pith.science (2026). https://pith.science/paper/YBCC6ICF

@misc{pith2026260801318,
  author       = {Pith},
  title        = {Pith review of: Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YBCC6ICF}},
  note         = {Machine review of arXiv:2608.01318}
}

read the original abstract

Modern sensing, communication, and learning systems generate heterogeneous network signals, with local data differing in dimension, modality, and geometric structure. Processing such data requires a mathematical framework capable of simultaneously modeling heterogeneous local signal spaces and the transformations relating them. Network sheaves provide such a framework by associating local vector spaces with network entities and linear restriction maps with their interactions. This is the first paper to develop a unified sheaf signal processing (SSP) framework on network sheaves, extending the fundamental operations of signal processing, namely spectral analysis, filtering, and sampling, to heterogeneous local spaces. Unlike graph and topological signal processing, where signals are modeled over a common vector space, SSP jointly models heterogeneous local signal spaces and the linear transformations relating neighboring spaces through restriction maps. We define the Sheaf Fourier Transform (SFT), whose frequencies quantify signal inconsistency induced by the network topology, the restriction maps, and the local geometry. Building on this representation, we develop polynomial sheaf filters and formulate sampling as the joint selection of network nodes and intra-node components. We derive perfect recovery conditions for bandlimited sheaf signals and propose a greedy sampling-set design algorithm. To incorporate application-dependent signal models, including different bases, dictionaries, and learned embeddings, we introduce representation sheaves and characterize the natural transformations that preserve spectral properties and guarantee interoperability across representations. Experiments on synthetic, motion-capture, and financial datasets validate the proposed framework and demonstrate consistent improvements over canonical graph signal processing baselines.

Figures

Figures reproduced from arXiv: 2608.01318 by the authors.

**Figure 1.** Dictionaries as components of the natural transformation δ [15] between the representation sheaf J and the signal sheaf F over the edge e = (i, j). conditions does a collection of local dictionary representations induce a consistent low-dimensional network sheaf? Specifically, let the signal attached to node i admit the representation xi = Disi , si ∈ R ci , ci ≤ di , (7) where Di ∈ R di×ci is a dictionary associat… view at source ↗

**Figure 2.** Sensor network topology of the filtering experiment. [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Reconstruction error (left panel) and fraction of [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: NMSE versus relative bandwidth, for different SNR [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: (a) Reconstruction error (NMSE) vs number of [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

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2022
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Tangent bundle convolutional learning: From manifolds to cellular sheaves and back,

C. Battiloro, Z. Wang, H. Riess, P. Di Lorenzo, and A. Ribeiro, “Tangent bundle convolutional learning: From manifolds to cellular sheaves and back,”IEEE Trans. on Signal Processing, vol. 72, pp. 1892–1909, 2024

1909
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Consistent geometric deep learning via Hilbert bundles and cellular sheaves,

K. Tandon, J. Gould, T. Bhatia, F. Dominici, A. Ribeiro, and C. Battiloro, “Consistent geometric deep learning via Hilbert bundles and cellular sheaves,”arXiv preprint arXiv:2605.06395, 2026

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Cellular sheaves of lattices and the Tarski Laplacian,

R. Ghrist and H. Riess, “Cellular sheaves of lattices and the Tarski Laplacian,”Homology, Homotopy and Applications, vol. 24, no. 1, 2022

2022
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Learning network sheaves for AI-native semantic communication,

E. Grimaldi, M. E. Pandolfo, G. D’Acunto, S. Barbarossa, and P. Di Lorenzo, “Learning network sheaves for AI-native semantic communication,” in2025 59th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2025, pp. 1692–1696

2025
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Learning consistent causal abstraction networks,

——, “Learning consistent causal abstraction networks,” inProc. of IEEE ICASSP 2026, Barcelona, Spain

2026
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Sampling and recovery of graph signals,

P. Di Lorenzo, S. Barbarossa, and P. Banelli, “Sampling and recovery of graph signals,” inCooperative and Graph Signal Processing, 2018

2018
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An analysis of ap- proximations for maximizing submodular set functions,

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Learning Laplacian matrix in smooth graph signal representations,

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Performance measurement with the arbitrage pricing theory: A new framework for analysis,

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Networks of causal abstractions: A sheaf-theoretic framework,

G. D’Acunto, P. Di Lorenzo, and S. Barbarossa, “Networks of causal abstractions: A sheaf-theoretic framework,”arXiv preprint arXiv:2509.25236, 2026

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Ranking and sparsifying a connection graph,

F. Chung, W. Zhao, and M. Kempton, “Ranking and sparsifying a connection graph,”Internet Mathematics, vol. 10, no. 1-2, pp. 87–115, 2014

2014

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Goal-oriented and semantic communication in 6G AI-native networks: The 6G-GOALS approach,

E. C. Strinati, P. Di Lorenzoet al., “Goal-oriented and semantic communication in 6G AI-native networks: The 6G-GOALS approach,” in2024 Joint European Conference on Networks and Communications & 6G Summit. IEEE, 2024, pp. 1–6

work page 2024

[2] [2]

The emerging field of signal processing on graphs: Ex- tending high-dimensional data analysis to networks and other irregular domains,

D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega, and P. Van- dergheynst, “The emerging field of signal processing on graphs: Ex- tending high-dimensional data analysis to networks and other irregular domains,”IEEE Signal Processing Mag., vol. 30, no. 3, pp. 83–98, 2013

work page 2013

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Graph signal processing: Overview, challenges, and applications,

A. Ortega, P. Frossard, J. Kova ˇcevi´c, J. M. Moura, and P. Vandergheynst, “Graph signal processing: Overview, challenges, and applications,”Pro- ceedings of the IEEE, vol. 106, no. 5, pp. 808–828, 2018

2018

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Discrete signal processing on graphs,

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

2013

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Signals on graphs: Uncertainty principle and sampling,

M. Tsitsvero, S. Barbarossa, and P. Di Lorenzo, “Signals on graphs: Uncertainty principle and sampling,”IEEE Trans. on Signal Processing, vol. 64, no. 18, pp. 4845–4860, 2016

work page 2016

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Connecting the dots: Identifying network structure via graph signal processing,

G. Mateos, S. Segarra, A. G. Marques, and A. Ribeiro, “Connecting the dots: Identifying network structure via graph signal processing,”IEEE Signal Processing Mag., vol. 36, no. 3, pp. 16–43, 2019

work page 2019

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On the graph Fourier transform for directed graphs,

S. Sardellitti, S. Barbarossa, and P. Di Lorenzo, “On the graph Fourier transform for directed graphs,”IEEE Journal of Selected Topics in Signal Processing, vol. 11, no. 6, pp. 796–811, 2017

work page 2017

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Adaptive graph signal processing: Algorithms and optimal sampling strategies,

P. Di Lorenzo, P. Banelli, E. Isufi, S. Barbarossa, and G. Leus, “Adaptive graph signal processing: Algorithms and optimal sampling strategies,” IEEE Trans. on Signal Processing, vol. 66, no. 13, pp. 3584–3598, 2018

2018