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arxiv: 2606.05490 · v1 · pith:2RIPLFMFnew · submitted 2026-06-03 · 🧮 math.OC

Optimal experimental design for passive imaging source problems

Christian Aarset , Thorsten Hohage , Georg Stadler This is my paper

Pith reviewed 2026-06-28 04:44 UTC · model grok-4.3

classification 🧮 math.OC
keywords optimal experimental designpassive imagingBayesian inverse problemsA-optimal designlow-rank approximationHelmholtz equationsensor placement
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The pith

A two-level low-rank approximation of the A-optimal design objective decouples passive imaging problems into offline and online phases that require no additional PDE solves.

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

The paper develops an efficient method for choosing sensor locations in passive imaging source problems posed as Bayesian inverse problems governed by the Helmholtz equation. Correlation-based observations cause the data dimension to grow quadratically with the number of sensors, making repeated PDE solves in standard optimal design algorithms prohibitively expensive. The authors introduce a two-level low-rank approximation to the A-optimal design objective that separates an expensive offline stage from a cheap online stage. This separation allows rapid evaluation of both the design objective and its gradient. Numerical tests indicate that the resulting designs reduce posterior uncertainty more effectively than random sensor placements while scaling to large problem sizes.

Core claim

We develop a two-level, low-rank approximation of the A-optimal design objective. This effectively decouples the problem into an offline and an online phase, enabling efficient evaluation of the design objective and its gradient without additional PDE solves. Our numerical results demonstrate that the proposed algorithm efficiently scales to large problems and that the resulting optimal designs significantly outperform random sensor placements in minimizing posterior uncertainty.

What carries the argument

Two-level low-rank approximation of the A-optimal design objective, which separates offline computation from online evaluation.

If this is right

  • Design objective and gradient can be evaluated without any additional PDE solves once the offline phase is complete.
  • The approach scales to large numbers of candidate sensor locations because the online phase cost is independent of the PDE dimension.
  • Optimal sensor placements identified this way produce measurably lower posterior uncertainty than random placements.
  • The method applies directly to spatially uncorrelated sources in Helmholtz-governed passive imaging.

Where Pith is reading between the lines

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

  • The offline-online split may extend to other inverse problems whose observation operators admit low-rank structure.
  • Real-time re-optimization of sensor placements becomes feasible once the offline matrices are precomputed.
  • The same decoupling could reduce cost in related wave-based imaging settings such as seismic or ultrasound source localization.

Load-bearing premise

The low-rank approximation of the A-optimal objective remains sufficiently accurate across the range of designs considered.

What would settle it

A direct numerical comparison on a test problem showing that a design selected by the approximated objective yields higher true posterior variance than a design selected by the exact objective or by a competing method.

Figures

Figures reproduced from arXiv: 2606.05490 by Christian Aarset, Georg Stadler, Thorsten Hohage.

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Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
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Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
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Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
read the original abstract

This work focuses on optimal experimental design (OED) methods for passive imaging. We adopt a Bayesian inverse problem framework for passive imaging source problems, primarily focusing on spatially uncorrelated sources and systems governed by the Helmholtz equation. A major challenge in passive imaging is that the use of correlation data causes the observation dimension to grow quadratically with the number of sensor locations, compounding the computational difficulty of finding optimal designs. To overcome the computational bottleneck of repeated PDE solves in optimal design algorithms, we develop a two-level, low-rank approximation of the A-optimal design objective. This effectively decouples the problem into an offline and an online phase, enabling efficient evaluation of the design objective and its gradient without additional PDE solves. Our numerical results demonstrate that the proposed algorithm efficiently scales to large problems and that the resulting optimal designs significantly outperform random sensor placements in minimizing posterior uncertainty.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript develops a two-level low-rank approximation to the A-optimal design objective for Bayesian inverse problems arising in passive imaging of spatially uncorrelated sources governed by the Helmholtz equation. The approximation decouples the problem into offline and online phases, enabling evaluation of the design objective and its gradient without additional PDE solves during optimization. Numerical results are presented to demonstrate scalability to large problems and that the resulting designs significantly outperform random sensor placements in reducing posterior uncertainty.

Significance. If the low-rank approximation is shown to preserve design optimality rankings, the approach would address the quadratic growth in observation dimension that arises from using correlation data in passive imaging, enabling practical OED at scales where repeated PDE solves are prohibitive. The work applies standard Bayesian OED and low-rank techniques to this setting; credit is due for the explicit offline/online decoupling tailored to the correlation-data observation model.

major comments (2)
  1. [Abstract] Abstract and numerical results section: The claim that the resulting optimal designs 'significantly outperform random sensor placements' is not accompanied by quantitative error bounds on the two-level low-rank approximation, perturbation analysis, or numerical checks confirming that approximation error does not reorder candidate designs or inflate the reported posterior-uncertainty reduction.
  2. [Numerical experiments] The central claim that online-phase evaluations reliably identify designs minimizing posterior uncertainty rests on the unverified assumption that the low-rank approximation remains sufficiently accurate across the range of designs considered; no validation details, test-case descriptions, or accuracy metrics are provided to support this.
minor comments (1)
  1. [Methods] Notation for the observation operator and covariance in the correlation-data setting could be clarified with an explicit equation reference early in the methods section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback. The comments correctly identify the need for stronger validation of the two-level low-rank approximation to support the claims regarding design performance. We address each major comment below and will revise the manuscript to incorporate the requested analysis and metrics.

read point-by-point responses

  1. Referee: [Abstract] Abstract and numerical results section: The claim that the resulting optimal designs 'significantly outperform random sensor placements' is not accompanied by quantitative error bounds on the two-level low-rank approximation, perturbation analysis, or numerical checks confirming that approximation error does not reorder candidate designs or inflate the reported posterior-uncertainty reduction.

    Authors: We agree that the manuscript would benefit from quantitative error bounds, perturbation analysis, and explicit numerical checks confirming that the approximation does not reorder designs or inflate the reported uncertainty reductions. In the revised version we will add a dedicated subsection on approximation error that includes (i) a perturbation analysis relating the low-rank error to the A-optimal objective, (ii) computable a-posteriori error indicators, and (iii) numerical verification on representative design candidates that compares the approximated objective values against reference values obtained with higher-rank or full-order models. These additions will directly support the claim that the reported performance gains are not artifacts of the approximation. revision: yes

  2. Referee: [Numerical experiments] The central claim that online-phase evaluations reliably identify designs minimizing posterior uncertainty rests on the unverified assumption that the low-rank approximation remains sufficiently accurate across the range of designs considered; no validation details, test-case descriptions, or accuracy metrics are provided to support this.

    Authors: We acknowledge that the current numerical experiments section does not supply the requested validation details. We will expand this section with (i) explicit descriptions of the test cases used for accuracy assessment, (ii) quantitative accuracy metrics (relative errors in the objective and its gradient) evaluated on a grid of designs spanning the optimization trajectory, and (iii) direct comparisons between the two-level approximation and a higher-fidelity reference for a subset of candidate sensor placements. These additions will substantiate that the online-phase evaluations remain reliable for identifying designs that minimize posterior uncertainty. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation builds on standard OED and low-rank methods

full rationale

The paper presents a two-level low-rank approximation to the A-optimal objective for Bayesian OED in passive imaging source problems governed by the Helmholtz equation. This approximation is introduced as a new computational technique that decouples offline and online phases, with efficiency and outperformance over random designs demonstrated via numerical results rather than by algebraic identity or self-referential fitting. No load-bearing step reduces a claimed prediction or uniqueness result to a parameter fitted from the same data, a self-citation chain, or an ansatz smuggled from prior author work; the central claims remain independent of the inputs they evaluate.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated.

pith-pipeline@v0.9.1-grok · 5668 in / 942 out tokens · 25562 ms · 2026-06-28T04:44:42.851816+00:00 · methodology

discussion (0)

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Works this paper leans on

106 extracted references · 33 canonical work pages

  1. [1]

    Inverse Problems , month =

    Björn Müller and Thorsten Hohage and Damien Fournier and Laurent Gizon , title =. Inverse Problems , month =. doi:10.1088/1361-6420/ad2b9a , number =

    work page doi:10.1088/1361-6420/ad2b9a

  2. [2]

    2026 , eprint=

    H\"older-Logarithmic Stability and Convergence Rates for an Inverse Random Source Problem , author=. 2026 , eprint=

    2026

  3. [3]

    and Kress, R

    Colton, D. and Kress, R. , title =

  4. [4]

    and McKeague, I

    Baker, C. and McKeague, I. , title =. Proceedings of the American Mathematical Society , volume =

  5. [5]

    , title =

    Stuart, A. , title =. Acta Numerica , volume =

  6. [6]

    , title =

    Alexanderian, A. , title =. Inverse Problems , volume =

  7. [7]

    Shurbet, G. L. and Lewis, T. O. and Boullion, T. L. , title =. The Ohio Journal of Science , volume =

  8. [8]

    Toland, J. F. , title =

  9. [9]

    Biometrika , volume =

    Wishart, John , title =. Biometrika , volume =. 1928 , month =. doi:10.1093/biomet/20A.1-2.32 , url =

    work page doi:10.1093/biomet/20a.1-2.32 1928

  10. [10]

    Properties of the singular, inverse and generalized inverse partitioned Wishart distributions , journal =

    Taras Bodnar and Yarema Okhrin , keywords =. Properties of the singular, inverse and generalized inverse partitioned Wishart distributions , journal =. 2008 , issn =. doi:https://doi.org/10.1016/j.jmva.2008.02.024 , url =

    work page doi:10.1016/j.jmva.2008.02.024 2008

  11. [11]

    , title =

    Srivastava, S. , title =. Ann. Statist. , volume =

  12. [12]

    Kelley, J. L. , title =. 1955 , publisher =

    1955

  13. [13]

    , title =

    Hohage, T. , title =

  14. [14]

    Muirhead, R. J. , title =. 1982 , publisher =

    1982

  15. [15]

    , title =

    Bentkus, V. , title =. Theory of Probability & Its Applications , volume =. 2005 , doi =. https://doi.org/10.1137/S0040585X97981123 , abstract =

    work page doi:10.1137/s0040585x97981123 2005

  16. [16]

    , title =

    Giambartolomei, G. , title =

  17. [17]

    Passive Imaging with Ambient Noise , publisher=

    Garnier, Josselin and Papanicolaou, George , year=. Passive Imaging with Ambient Noise , publisher=

  18. [18]

    Physics of Fluids , volume =

    Moreau, Stéphane , title = ". Physics of Fluids , volume =. 2022 , month =. doi:10.1063/5.0084060 , url =

    work page doi:10.1063/5.0084060 2022

  19. [19]

    An optimal experimental design strategy for improving parameter estimation in stochastic models , journal =

    Chunbing Huang and Federica Cattani and Federico Galvanin , keywords =. An optimal experimental design strategy for improving parameter estimation in stochastic models , journal =. 2023 , issn =. doi:https://doi.org/10.1016/j.compchemeng.2023.108133 , url =

    work page doi:10.1016/j.compchemeng.2023.108133 2023

  20. [20]

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

    Beck, Amir and Teboulle, Marc , title =. SIAM Journal on Imaging Sciences , volume =. 2009 , doi =. https://doi.org/10.1137/080716542 , abstract =

    work page doi:10.1137/080716542 2009

  21. [21]

    Halko, P

    Halko, N. and Martinsson, P. G. and Tropp, J. A. , title =. SIAM Rev. , keywords =. doi:10.1137/090771806 , issn =

    work page doi:10.1137/090771806

  22. [22]

    2014 , url=

    C++11 Implementation of Finite Elements in NGSolve , author=. 2014 , url=

    2014

  23. [23]

    SIAM/ASA Journal on Uncertainty Quantification , volume =

    Alexanderian, Alen and Petra, Noemi and Stadler, Georg and Sunseri, Isaac , title =. SIAM/ASA Journal on Uncertainty Quantification , volume =. 2021 , doi =. https://doi.org/10.1137/20M1347292 , abstract =

    work page doi:10.1137/20m1347292 2021

  24. [24]

    , title =

    Herman, Elizabeth and Alexanderian, Alen and Saibaba, Arvind K. , title =. SIAM Journal on Scientific Computing , volume =. 2020 , doi =

    2020

  25. [25]

    and Veroy, Karen , booktitle =

    Aretz-Nellesen, Nicole and Chen, Peng and Grepl, Martin A. and Veroy, Karen , booktitle =. A Sequential Sensor Selection Strategy for Hyper-Parameterized Linear

  26. [26]

    A greedy sensor selection algorithm for hyperparameterized linear

    Nicole Aretz and Peng Chen and Denise Degen and Karen Veroy , keywords =. A greedy sensor selection algorithm for hyperparameterized linear. Journal of Computational Physics , volume =. 2024 , issn =. doi:https://doi.org/10.1016/j.jcp.2023.112599 , url =

    work page doi:10.1016/j.jcp.2023.112599 2024

  27. [27]

    Towards optimal sensor placement for inverse problems in spaces of measures , volume =

    Huynh, Phuoc-Truong and Pieper, Konstantin and Walter, Daniel , year =. Towards optimal sensor placement for inverse problems in spaces of measures , volume =. Inverse Problems , doi =

  28. [28]

    Large-Scale

    Wu, Keyi and O’Leary-Roseberry, Thomas and Chen, Peng and Ghattas, Omar , year =. Large-Scale. Journal of Scientific Computing , doi =

  29. [29]

    Israel Gohberg and Seymour Goldberg and Nahum Krupnik , title =

  30. [30]

    SIAM Journal on Scientific Computing , year =

    Alexanderian, Alen and Petra, Noemi and Stadler, Georg and Ghattas, Omar , title =. SIAM Journal on Scientific Computing , year =. doi:10.1137/130933381 , eprint =

    work page doi:10.1137/130933381

  31. [31]

    SIAM Journal on Scientific Computing , volume =

    Alexanderian, Alen and Petra, Noemi and Stadler, Georg and Ghattas, Omar , title =. SIAM Journal on Scientific Computing , volume =. 2016 , doi =. https://doi.org/10.1137/140992564 , abstract =

    work page doi:10.1137/140992564 2016

  32. [32]

    Brislawn, Chris , title =. Proc. Amer. Math. Soc. , volume =. 1988 , doi =

    1988

  33. [33]

    On information and sufficiency,

    Sherman, Jack and Morrison, Winnifred J. , title =. The Annals of Mathematical Statistics , publisher =. doi:10.1214/aoms/1177729893 , number =

    work page doi:10.1214/aoms/1177729893

  34. [34]

    A. D. Agaltsov and T. Hohage and R. G. Novikov , title =. Inverse Problems , month =. doi:10.1088/1361-6420/ab77d9 , number =

    work page doi:10.1088/1361-6420/ab77d9

  35. [35]

    2017 , PAGES =

    Isakov, Victor , title =. doi:10.1007/978-3-319-51658-5 , isbn =

    work page doi:10.1007/978-3-319-51658-5

  36. [36]

    , year = 1997, series =

    Conway, John B. , title =. 2007 , publisher =. doi:10.1007/978-1-4757-4383-8 , isbn =

    work page doi:10.1007/978-1-4757-4383-8 2007

  37. [37]

    SIAM Journal on Scientific Computing , volume =

    Bui-Thanh, Tan and Ghattas, Omar and Martin, James and Stadler, Georg , title =. SIAM Journal on Scientific Computing , volume =. 2013 , doi =. https://doi.org/10.1137/12089586X , abstract =

    work page doi:10.1137/12089586x 2013

  38. [38]

    and Alexanderian, Alen and Ipsen, Ilse C

    Saibaba, Arvind K. and Alexanderian, Alen and Ipsen, Ilse C. F. , title =. Numerische Mathematik , month =. doi:10.1007/s00211-017-0880-z , issn =

    work page doi:10.1007/s00211-017-0880-z

  39. [39]

    2011 , doi =

    Saad, Yousef , title =. 2011 , doi =

    2011

  40. [40]

    , title =

    Gu, M. , title =. SIAM Journal on Scientific Computing , volume =. 2015 , doi =. https://doi.org/10.1137/130938700 , abstract =

    work page doi:10.1137/130938700 2015

  41. [41]

    and Hart, Joseph and van Bloemen Waanders, Bart , title =

    Saibaba, Arvind K. and Hart, Joseph and van Bloemen Waanders, Bart , title =. Numerical Linear Algebra with Applications , volume =. doi:https://doi.org/10.1002/nla.2364 , url =. https://onlinelibrary.wiley.com/doi/pdf/10.1002/nla.2364 , abstract =

    work page doi:10.1002/nla.2364

  42. [42]

    The Effect of Finite Element Discretisation on the Stationary Distribution of

    Voss, Jochen , journal =. The Effect of Finite Element Discretisation on the Stationary Distribution of

  43. [43]

    2017 , doi =

    Beck, Amir , title =. 2017 , doi =

    2017

  44. [44]

    GRAM-SCHMIDT PROCESS OF ORTHONORMALIZATION IN BANACH SPACES , urldate =

    Lin, Ying-Hsiung , journal =. GRAM-SCHMIDT PROCESS OF ORTHONORMALIZATION IN BANACH SPACES , urldate =

  45. [45]

    SIAM/ASA Journal on Uncertainty Quantification , volume =

    Wu, Keyi and Chen, Peng and Ghattas, Omar , title =. SIAM/ASA Journal on Uncertainty Quantification , volume =. 2023 , doi =. https://doi.org/10.1137/21M1466499 , abstract =

    work page doi:10.1137/21m1466499 2023

  46. [46]

    Chan , abstract =

    Tony F. Chan , abstract =. Rank revealing QR factorizations , journal =. 1987 , issn =. doi:https://doi.org/10.1016/0024-3795(87)90103-0 , url =

    work page doi:10.1016/0024-3795(87)90103-0 1987

  47. [47]

    Tr\"oltzsch , date =

    F. Tr\"oltzsch , date =. Optimal Control of Partial Differential Equations: Theory, Methods and Applications , publisher =

  48. [48]

    Philosophical Transactions of the Royal Society of London , title =

    Mercer, James and Forsyth, Andrew Russell , year =. Philosophical Transactions of the Royal Society of London , title =. doi:10.1098/rsta.1909.0016 , number =

    work page doi:10.1098/rsta.1909.0016 1909

  49. [49]

    , year =

    Ucinski, D. , year =. Optimal Measurement Methods for Distributed Parameter System Identification , doi =

  50. [50]

    Schur , date =

    J. Schur , date =. Bemerkungen zur Theorie der beschränkten Bilinearformen mit unendlich vielen Veränderlichen. , doi =

  51. [51]

    Trace ideals and their applications , url =

    Barry Simon , date =. Trace ideals and their applications , url =

  52. [52]

    Multidimensional sum-up rounding for integer programming in optimal experimental design , doi =

    Yu, Jing and Anitescu, Mihai , date =. Multidimensional sum-up rounding for integer programming in optimal experimental design , doi =

  53. [53]

    Henderson, H. V. and Searle, S. R. , year =. SIAM Review , title =. doi:10.1137/1023004 , eprint =

    work page doi:10.1137/1023004

  54. [54]

    The norm of the Schur product operation , doi =

    Davis, Chandler , date =. The norm of the Schur product operation , doi =

  55. [55]

    Welch , date =

    William J. Welch , date =. Branch-and-Bound Search for Experimental Designs Based on D Optimality and Other Criteria , issn =

  56. [56]

    A branch-and-bound algorithm for the exact optimal experimental design problem , doi =

    Ahipaşaoğlu, Selin Damla , date =. A branch-and-bound algorithm for the exact optimal experimental design problem , doi =

  57. [57]

    H. W. Engl and M. Hanke and A. Neubauer , date =. Regularization of Inverse Problems , publisher =

  58. [58]

    Kiefer , date =

    J. Kiefer , date =. General Equivalence Theory for Optimum Designs (Approximate Theory) , issn =

  59. [59]

    Elfving , date =

    G. Elfving , date =. Optimum Allocation in Linear Regression Theory , issn =

  60. [60]

    Elfving , date =

    G. Elfving , date =. Design of linear experiments , pages =

  61. [61]

    Compressed Sensing: Theory and Applications , publisher =

  62. [62]

    Alberti and Alessandro Felisi and Matteo Santacesaria and S

    Giovanni S. Alberti and Alessandro Felisi and Matteo Santacesaria and S. Ivan Trapasso , date =. Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform , eprint =

  63. [63]

    Randomized algorithms for the low-rank approximation of matrices , doi =

    Edo Liberty and Franco Woolfe and Per-Gunnar Martinsson and Vladimir Rokhlin and Mark Tygert , date =. Randomized algorithms for the low-rank approximation of matrices , doi =. https://www.pnas.org/doi/pdf/10.1073/pnas.0709640104 , number =

    work page doi:10.1073/pnas.0709640104

  64. [64]

    Convex analysis , edition =

    Rockafellar, Ralph Tyrrell , date =. Convex analysis , edition =

  65. [65]

    , date =

    Bertsekas, Dimitri P. , date =. Nonlinear programming , edition =

  66. [66]

    Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs , doi =

    Karina Koval and Alen Alexanderian and Georg Stadler , date =. Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs , doi =

  67. [67]

    Numerical methods for A-optimal designs with a sparsity constraint for ill-posed inverse problems , doi =

    Haber, Eldad and Magnant, Zhuojun and Lucero, Christian and Tenorio, Luis , date =. Numerical methods for A-optimal designs with a sparsity constraint for ill-posed inverse problems , doi =

  68. [68]

    Pukelsheim.Optimal design of experiments

    Pukelsheim, Friedrich , date =. Optimal Design of Experiments , doi =. https://epubs.siam.org/doi/pdf/10.1137/1.9780898719109 , publisher =

    work page doi:10.1137/1.9780898719109

  69. [69]

    C++ 11 implementation of finite elements in NGSolve , volume =

    Sch. C++ 11 implementation of finite elements in NGSolve , volume =

  70. [70]

    SLSQP , url =

    SciPy , date =. SLSQP , url =

  71. [71]

    Inverse Problems and Imaging , title =

    Yair Daon and Georg Stadler , year =. Inverse Problems and Imaging , title =. doi:10.3934/ipi.2018045 , issn =

    work page doi:10.3934/ipi.2018045

  72. [72]

    A note on the relationship between

    Umberto Villa and Thomas O'Leary-Roseberry , date =. A note on the relationship between

  73. [73]

    , date =

    Helmholtz, H. , date =. Theorie der Luftschwingungen in Röhren mit offenen Enden. , language =

  74. [74]

    , date =

    Banachiewicz, T. , date =. M\'ethode de r\'esolution num\'erique des \'equations lin\'eaires , pages =

  75. [75]

    Global optimality conditions for sensor placement, with extensions to binary low-rank

    Aarset, Christian , journal=. Global optimality conditions for sensor placement, with extensions to binary low-rank. 2025 , publisher=

    2025

  76. [76]

    Raumer, Hans-Georg , title =

  77. [77]

    Acoustical Physics , Year =

    A three-dimensional tomography model for reconstruction of oceanic inhomogeneities under unknown antenna positioning , Author =. Acoustical Physics , Year =. doi:10.1134/S1063771011020035 , ISSN =

    work page doi:10.1134/s1063771011020035

  78. [78]

    Imaging passive seismic data , author=

  79. [79]

    A Comparison of Strategies for Seismic Interferometry , year =

    Snieder, Roel and Miyazawa, Masatoshi and Slob, Evert and Vasconcelos, Ivan and Wapenaar, Kees , journal =. A Comparison of Strategies for Seismic Interferometry , year =. doi:10.1007/s10712-009-9069-z , owner =

    work page doi:10.1007/s10712-009-9069-z

  80. [80]

    Nature , Year =

    Time-distance helioseismology , Author =. Nature , Year =

Showing first 80 references.