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Deep Learning VLBI Image Reconstruction with Closure Invariants

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A deep network called DIReCT reconstructs VLBI images directly from calibration-free closure invariants, reaching a median fidelity of about 0.92 on untrained source morphologies.

desk verdict A promising proof-of-concept for direct VLBI imaging from closure invariants, but the network never enforces data consistency, so the central claim is currently overreaching. read the letter →

arxiv 2411.12233 v1 pith:WUAMJKVF submitted 2024-11-19 astro-ph.IM

Samuel Lai , Nithyanandan Thyagarajan , O. Ivy Wong , Foivos Diakogiannis , Lucas Hoefs This is my paper · ORCID
classification astro-ph.IM
keywords closureinvariantsVLBIimagingdeeplearningimagereconstructioninterferometryphasestransformerEventHorizonTelescope
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

Very long baseline interferometry measures only sparse Fourier samples of a source, and the usual calibration of station gains is a delicate iterative process. Closure invariants—quantities built from loops of baselines—are immune to station-based corruptions, but the reverse map from these invariants to an image was not established. This paper establishes it with a deep network called DIReCT, trained on natural images and simple geometric shapes, that maps the complete set of co-polar closure invariants directly to a source image. The network reconstructs untrained morphologies with a median normalized cross-correlation fidelity around 0.92, is insensitive to arbitrary gain errors, and is robust to thermal noise down to moderate levels—all without hand-tuned hyperparameters per prediction. A sympathetic reader would care because this offers a calibration-independent, fast imaging channel that can cross-check and initialize conventional VLBI reconstructions.

What carries the argument

The central object is the complete set of real-valued closure invariants arising from the Abelian gauge formalism of Thyagarajan et al. (2022): each triangular loop of baselines pinned to a reference station defines a complex advariant, and normalising away the reference gain yields the full independent set of closure phases and closure amplitudes as a single unified list. The load-bearing mechanism is a transformer encoder feeding a convolutional autoencoder: the image encoder and the transformer are trained to produce matching latent vectors, so at inference the transformer must predict the latent code that the decoder turns into an image. The training objective mixes a latent mean-squared-error term, a class cross-entropy term, and image losses combining NRMSE and NXCORR, with a staged schedule that first centres the image and then relaxes to position-and-flux-insensitive fidelity.

What would settle it

Take a source whose morphology is deliberately far outside the training prior—for example, a high-contrast, multi-scale fractal or an extended jet with sharp transverse gradients—simulate noiseless closure invariants at EHT uv-coverage, and reconstruct with the trained DIReCT without any retraining. If the median fidelity on such out-of-prior sources collapses well below the roughly 0.9 seen for CIFAR-10-derived composites while classical regularised methods perform better, the claim that closure invariants support general-purpose direct reconstruction is contradicted and the network is shown to have learned the training prior rather than the inverse closure map.

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Extended reading notes

Core claim

The paper's claim is that the complete, independent set of co-polar closure invariants in the Thyagarajan et al. (2022) formalism carries enough information, under sparse EHT-like uv-coverage, to directly reconstruct the source intensity distribution—the missing inverse map to the known forward map from image to invariants. Using a convolutional autoencoder whose latent vector is also predicted by a transformer reading the invariant set, the model DIReCT is trained with a compound loss matching latent codes and images. On 10,000 random augmented composite morphologies never seen in training, the median NXCORR fidelity to the blurred ground truth is about 0.92, with the distribution mode near 0.95; fidelity stays above roughly 0.95 until thermal noise pushes the median closure-invariant SNR below about 10, then declines rapidly. The reconstructions are unchanged by arbitrarily large multiplicative station gains, because the invariants cancel those gains by construction. In side-by-side comparisons on noiseless synthetic observations, DIReCT is comparable to or better than CLEAN, eht-imaging, and DoG-HiT on classes similar to the training set, and remains competitive on untrained classes such as a Sagittarius A* accretion-flow model and a fourth-order m-ring.

Load-bearing premise

The load-bearing premise is that the training prior—mostly CIFAR-10 natural images plus simple tapered shapes—is representative enough of real VLBI source morphologies that the learned inverse mapping generalises; the authors explicitly note in Section 5 that this dataset forms the implicit prior and biases reconstructions toward centralised, smooth sources.

Editorial extensions

If this is right

  • A single trained DIReCT model produces an image from closure invariants in a fraction of a second, making it a practical rapid-imaging tool for monitoring programs that repeatedly observe the same field with a fixed array.
  • Because the input is calibration-independent by construction, DIReCT provides a cross-check on visibility-based reconstructions that does not share their gain-calibration assumptions.
  • Eliminating per-image hyperparameter tuning removes a source of user-dependent variability in sparse imaging, since the same trained weights apply to every prediction.
  • The paper's noise tests imply the approach can tolerate thermal noise up to about ten times the station SEFD before fidelity degrades, which covers many but not all realistic VLBI observations.
  • Extending the training set with noisy closure invariants, station-specific corruptions, and higher-order m-rings is the paper's stated path to fainter targets and more diverse morphologies.

Reading between the lines

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

  • The reported median fidelity on untrained composites is measured against the blurred ground truth, so part of the score rewards reproducing the beam-smoothed view; the unblurred fidelity is lower, and the method should not be read as resolving below the array beam without further evidence.
  • The dependence on a fixed array, pointing, and field of view means the method's generality is tied to its prior; a transfer-learning variant that adapts the transformer to new uv-coverage while freezing the decoder could extend the approach to other arrays at far lower cost than full retraining.
  • If DIReCT is applied to real M87 closure data, any systematic asymmetry bias in the recovered ring would directly reveal whether the CIFAR-10 prior's residual edge-orientation effects survive the rotational augmentations used in training.
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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

3 major / 6 minor

Summary. The paper presents DIReCT, a deep learning architecture that maps the complete set of co-polar closure invariants (Thyagarajan et al. 2022) directly to an image, trained on CIFAR-10 plus simple analytic shapes. The authors synthesize EHT-like uv-coverage, compute the closure invariants, and train a transformer encoder plus convolutional autoencoder with a four-term loss (classification, latent MSE, NRMSE, NXCORR). They validate the model on synthetic observations: insensitivity to station gain errors, robustness to thermal noise (reported via NXCORR and CRPS), a 10,000-image untrained-morphology test with median NXCORR about 0.92, and comparisons with CLEAN, eht-imaging, and DoG-HiT. The paper claims this establishes calibration-independent direct image reconstruction without per-prediction hyperparameter tuning.

Significance. Strengths: the paper ships reproducible code (DOI) and performs an unusually extensive synthetic validation (10,000 random morphologies, noise scaling over three orders of magnitude, comparisons with three established algorithms). If the claims hold, DIReCT would offer a fast, calibration-independent imaging path useful for monitoring programs such as MOJAVE, and it is a natural extension of the closure-invariant formalism. However, the central claim requires the reconstruction to be constrained by the input closure invariants; the current loss does not enforce this, so the significance is currently conditional.

major comments (3)
  1. [§4, Eq. (6), Fig. 7] The loss in Eq. (6) contains no term that compares the closure invariants of the reconstruction with the input closure invariants, and the paper states in §4 that the output is "not fit to the interferometric data explicitly". Figure 7 shows large closure-invariant residuals (SSE about 20 for the ring and m-ring rows) despite noiseless synthetic observations, so this residual is systematic rather than thermal. A reconstruction that does not reproduce its input data is not a solution to the inverse problem; the high NXCORR scores may reflect the training prior and decoder rather than the information contained in the closure invariants. This is load-bearing for the abstract's claim of "offers a calibration-independent constraint on source morphology". Please add a closure-invariant consistency metric (e.g., normalized SSE or closure NXCORR) to every reported test, and either add a data-consistency term or reframe the claim as "prior-based image synthesis conditioned on closure invariants" until consistency is demonstrated.
  2. [§3.4.2, Eq. (9), §4.2] The image loss in Eq. (9) includes 1−NXCORR, and beta is reduced to 0.5 in the final 100 epochs, so the network is explicitly trained to maximize the same NXCORR metric used for evaluation in Fig. 6. This is a form of metric overfitting: the median NXCORR of about 0.92 on untrained morphologies partly reflects the loss design rather than an independent measure of image fidelity. The paper should report complementary metrics (e.g., NRMSE, CRPS, or a structural similarity score) for the 10,000-morphology test, and ideally an ablation without the NXCORR loss term, to separate genuine reconstruction fidelity from alignment with the optimization target.
  3. [§3.4.1, §5, Fig. 8] The generalization evidence is narrower than the abstract's "general-purpose" wording. The 10,000 untrained morphologies are random combinations of the same primitive classes used in training (Gaussians, disks, ellipses, rings, m-rings, doubles), and the two real-astrophysics tests (the Sgr A* RIAF model and Centaurus A) show visible prior biases: Sgr A* is reconstructed as a crescent and Centaurus A as a "necktie knot", as the authors acknowledge. Demonstrating generalization on genuinely different source families (e.g., GRMHD snapshot images or jet simulations) with quantitative bias metrics would support the central claim, or the claims should be softened to sources that depart modestly from the training prior.
minor comments (6)
  1. [§2.1, after Eq. (5)] Please state explicitly that normalizing the advariants removes the absolute flux scale, since this is the reason DIReCT cannot recover total flux without further information.
  2. [§3.4.1] The counts of non-CIFAR training images are described only as "about 1000 from each class"; please give the exact number of shape images and the final training/validation split.
  3. [§4.1, Fig. 5 caption] The phrase "he effective beam" should read "the effective beam".
  4. [§5.2, Fig. 9] In the caption text, the image encoder latent is labeled (x_ci); this appears to be a typo for (x_ae), consistent with the notation used in the body.
  5. [§4.1] The sentence "it demonstrates satisfactory performance in fitting the data terms" is potentially misleading; suggest "reproducing the data terms approximately" since the model was not optimized for this.
  6. [§4.2, Fig. 6] The SSE values in the closure-invariant panels are shown for single examples; the text correctly cautions against cross-image comparison, so please add a per-image normalization or state explicitly that only within-panel residuals are meaningful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: DIReCT is a supervised inverse mapping with external generalization tests, and the self-cited closure formalism is background rather than a load-bearing circular premise.

full rationale

The paper's central claim is that a trained deep network can map closure invariants to images. This is a learned inverse mapping, not an analytical derivation from fitted constants. The training objective in Eq. (6) contains classification, latent-space, and image-space losses; the evaluation uses NXCORR, which also appears in the image loss, but the model is not fitting parameters to the test data, and the reported generalization to untrained morphologies is an external test. The paper explicitly admits that the output is 'not fit to the interferometric data explicitly' (Section 4, Figure 5 discussion), which is a data-consistency limitation rather than a circular step: no prediction is equivalent by construction to an input quantity. Self-citations to Thyagarajan et al. (2022) supply the closure-invariant formalism and Thyagarajan et al. (2024) supply prior classification work, but these are not used to forbid alternatives or to justify the reconstruction result; the formalism is an externally checkable mathematical construction and is not the thing being predicted. No equation in the paper reduces to its own input, and no fitted parameter is renamed as a prediction. Therefore the circularity score is 0.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

No new physical entities are postulated. The free parameters are hyperparameters of the neural network and loss function, chosen by validation or by hand. The key domain assumptions are the closure formalism, the noise model, and the representativeness of the training prior.

free parameters (5)
  • Loss weight vector alpha = [0.03, 1, 2, 3]
    Chosen after validating on a small selection of alternative hyperparameters (Section 3.4.2). Directly controls the balance between classification, latent, and image reconstruction losses.
  • NRMSE/NXCORR weighting beta = schedule: 1 for 50 epochs, 0.9 for next 100, 0.5 for last 100
    Hand-picked schedule to encourage centralized images first, then cross-correlation (Section 3.4.2).
  • Transformer encoder depth = 4 layers
    Architecture choice, not justified by ablation (Section 3.4).
  • Dropout rate = 0.10
    Set to prevent overfitting (Section 3.4.2).
  • Initial learning rate = 0.001, decay factor 0.99^n
    Standard choice; no sensitivity analysis (Section 3.4.2).
assumptions (4)
  • domain assumption Closure invariant formalism of Thyagarajan et al. (2022) provides a complete and independent set of calibration-independent invariants.
    The input representation is derived from this formalism; the paper relies on its correctness without re-deriving it (Section 2.1).
  • domain assumption Station-based multiplicative gain corruptions are the dominant systematic error, and additive thermal noise is Gaussian.
    Synthetic observation model used throughout (Section 2).
  • domain assumption CIFAR-10 natural images plus simple geometric shapes form a useful prior for astrophysical source morphologies.
    Adopted from Feng et al. (2024); the paper's generalization claims depend on this prior being sufficiently broad (Sections 3.4.1, 5).
  • ad hoc to paper The inverse mapping from closure invariants to images is learnable by the chosen transformer-autoencoder architecture.
    No theoretical guarantee; the paper demonstrates this empirically on synthetic data (Section 3.4).

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Cite this review

Pith. "Pith review of Deep Learning VLBI Image Reconstruction with Closure Invariants." pith.science (2026). https://pith.science/paper/WUAMJKVF

@misc{pith2026241112233,
  author       = {Pith},
  title        = {Pith review of: Deep Learning VLBI Image Reconstruction with Closure Invariants},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WUAMJKVF}},
  note         = {Machine review of arXiv:2411.12233}
}
abstract

Interferometric closure invariants, constructed from triangular loops of mixed Fourier components, capture calibration-independent information on source morphology. While a complete set of closure invariants is directly obtainable from measured visibilities, the inverse transformation from closure invariants to the source intensity distribution is not established. In this work, we demonstrate a deep learning approach, Deep learning Image Reconstruction with Closure Terms (DIReCT), to directly reconstruct the image from closure invariants. Trained on both well-defined mathematical shapes (two-dimensional gaussians, disks, ellipses, $m$-rings) and natural images (CIFAR-10), the results from our specially designed model are insensitive to station-based corruptions and thermal noise. The median fidelity score between the reconstruction and the blurred ground truth achieved is $\gtrsim 0.9$ even for untrained morphologies, where a unit score denotes perfect reconstruction. In our validation tests, DIReCT's results are comparable to other state-of-the-art deconvolution and regularised maximum-likelihood image reconstruction algorithms, with the advantage that DIReCT does not require hand-tuned hyperparameters for each individual prediction. This independent approach shows promising results and offers a calibration-independent constraint on source morphology, ultimately complementing and improving the reliability of sparse VLBI imaging results.

Figures

Figures reproduced from arXiv: 2411.12233 by the authors.

Figure 1
Figure 1. Illustration of the machine-learning architecture adopted in this study. During training, images are fed into a convolutional encoder with residual connections to produce a compressed information-rich representation, which is also predicted by a transformer encoder that accepts a set of closure invariants produced by synthetic observation with a VLBI array as input. The latent space can be used to reconstruct the im… view at source ↗
Figure 2
Figure 2. Illustration of the sampling function on the 𝑢𝑣-plane under rotation synthesis for a pointing location of RA = 12h30m49.42s and Dec = +12◦23′28.04′′ (J2000), and the resulting dirty beam. Observations are synthesised with short 5s integrations every 10 minutes over a period of 24 hours on 2017-04-05. Rotation synthesis curves are labeled with the associated station pairs. All images shown in this study share the sam… view at source ↗
Figure 3
Figure 3. (Top left) Ground truth image of a crescent represented by a first order 𝑚-ring (Roelofs et al. 2023). (Top middle) Ground truth blurred by the effective beam. (Top right) Illustration of the sensitivity in the normalised cross-correlation fidelity to gain error for regularised maximum-likelihood reconstructions using visibilities and closure invariants using eht-imaging, compared with our deep learning model (DIReC… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: (Left panel) Ground truth image of a Sagittarius A* radiatively inefficient accretion flow model (Broderick et al. 2011). (Left inset) RMS image illustrating the correlated noise introduced when the thermal noise level is set to 10× the SEFD. (Middle panel) Mean recons…
Figure 5
Figure 5. Figure 5: (Left) Models of 3C279 (top) and Centaurus A (bottom) seen within the field of view of the DIReCT model (225 × 225 𝜇as). The size scale and he effective beam size of our 𝑢𝑣-coverage are shown in the ground truth panel. The image reconstructed from synthetic observation…
Figure 6
Figure 6. Figure 6: (Left) NXCORR probability distribution for image reconstructions of 10,000 random augmented image combinations representing untrained source morphologies. The 16% and 84% percentiles are marked by the dashed line and the median by the solid line with their correspondin…
Figure 7
Figure 7. Figure 7: Image reconstructions of sample images representing distinct morphological classes of the training dataset with state-of-the-art methods (standard CLEAN, eht-imaging, DoG-HiT) compared to our trained machine learning model, DIReCT. We show the effective beam dimensions…
Figure 8
Figure 8. Figure 8: Same construction as in [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Pair-wise cosine comparison matrix of latent encoded features generated from closure invariants (𝑥ci) and images (𝑥ae) for both trained and untrained morphological classes in Figures 7 and 8, respectively. Similarity scores are distinguished by shade and scores above 7…

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Reference graph

Works this paper leans on

84 extracted references · 21 canonical work pages · cited by 1 Pith paper

  1. [1]

    Akiyama K., et al., 2017a, @doi [ ] 10.3847/1538-3881/aa6302 , https://ui.adsabs.harvard.edu/abs/2017AJ....153..159A 153, 159

    doi:10.3847/1538-3881/aa6302

  2. [2]

    Akiyama K., et al., 2017b, @doi [ ] 10.3847/1538-4357/aa6305 , https://ui.adsabs.harvard.edu/abs/2017ApJ...838....1A 838, 1

    doi:10.3847/1538-4357/aa6305

  3. [3]

    Arras P., Frank P., Haim P., Knollm \"u ller J., Leike R., Reinecke M., En lin T., 2022, @doi [Nature Astronomy] 10.1038/s41550-021-01548-0 , https://ui.adsabs.harvard.edu/abs/2022NatAs...6..259A 6, 259

    doi:10.1038/s41550-021-01548-0 2022

  4. [4]

    Baars J. W. M., Martin R. N., Mangum J. G., McMullin J. P., Peters W. L., 1999, @doi [ ] 10.1086/316365 , https://ui.adsabs.harvard.edu/abs/1999PASP..111..627B 111, 627

    work page doi:10.1086/316365 1999

  5. [5]

    D., Kloppenborg B., 2010, in Danchi W

    Baron F., Monnier J. D., Kloppenborg B., 2010, in Danchi W. C., Delplancke F., Rajagopal J. K., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 7734, Optical and Infrared Interferometry II. p. 77342I, @doi 10.1117/12.857364

    doi:10.1117/12.857364 2010

  6. [6]

    W., Johnson M

    Blackburn L., Pesce D. W., Johnson M. D., Wielgus M., Chael A. A., Christian P., Doeleman S. S., 2020, @doi [ ] 10.3847/1538-4357/ab8469 , https://ui.adsabs.harvard.edu/abs/2020ApJ...894...31B 894, 31

    doi:10.3847/1538-4357/ab8469 2020

  7. [7]

    E., Pesce D

    Broderick A. E., Pesce D. W., 2020, @doi [ ] 10.3847/1538-4357/abbd9d , https://ui.adsabs.harvard.edu/abs/2020ApJ...904..126B 904, 126

    work page doi:10.3847/1538-4357/abbd9d 2020

  8. [8]

    E., Fish V

    Broderick A. E., Fish V. L., Doeleman S. S., Loeb A., 2011, @doi [ ] 10.1088/0004-637X/735/2/110 , https://ui.adsabs.harvard.edu/abs/2011ApJ...735..110B 735, 110

    doi:10.1088/0004-637x/735/2/110 2011

Show all 84 references
  1. [9]

    E., Pesce D

    Broderick A. E., Pesce D. W., Tiede P., Pu H.-Y., Gold R., 2020, @doi [ ] 10.3847/1538-4357/ab9c1f , https://ui.adsabs.harvard.edu/abs/2020ApJ...898....9B 898, 9

    2020 doi

  2. [10]

    E., et al., 2022, @doi [ ] 10.3847/1538-4357/ac7c1d , https://ui.adsabs.harvard.edu/abs/2022ApJ...935...61B 935, 61

    Broderick A. E., et al., 2022, @doi [ ] 10.3847/1538-4357/ac7c1d , https://ui.adsabs.harvard.edu/abs/2022ApJ...935...61B 935, 61

    2022 doi

  3. [11]

    L., Thyagarajan N., 2022, @doi [ ] 10.3847/1538-4357/ac3cba , https://ui.adsabs.harvard.edu/abs/2022ApJ...924..125C 924, 125

    Carilli C. L., Thyagarajan N., 2022, @doi [ ] 10.3847/1538-4357/ac3cba , https://ui.adsabs.harvard.edu/abs/2022ApJ...924..125C 924, 125

    2022 doi

  4. [12]

    E., et al., 2011, @doi [ ] 10.1086/659879 , https://ui.adsabs.harvard.edu/abs/2011PASP..123..568C 123, 568

    Carlstrom J. E., et al., 2011, @doi [ ] 10.1086/659879 , https://ui.adsabs.harvard.edu/abs/2011PASP..123..568C 123, 568

    2011 doi

  5. [13]

    A., Johnson M

    Chael A. A., Johnson M. D., Narayan R., Doeleman S. S., Wardle J. F. C., Bouman K. L., 2016, @doi [ ] 10.3847/0004-637X/829/1/11 , https://ui.adsabs.harvard.edu/abs/2016ApJ...829...11C 829, 11

    2016 doi

  6. [14]

    A., Johnson M

    Chael A. A., Johnson M. D., Bouman K. L., Blackburn L. L., Akiyama K., Narayan R., 2018, @doi [ ] 10.3847/1538-4357/aab6a8 , https://ui.adsabs.harvard.edu/abs/2018ApJ...857...23C 857, 23

    2018 doi

  7. [15]

    J., 2008, @doi [IEEE Journal of Selected Topics in Signal Processing] 10.1109/JSTSP.2008.2006388 , 2, 793

    Cornwell T. J., 2008, @doi [IEEE Journal of Selected Topics in Signal Processing] 10.1109/JSTSP.2008.2006388 , 2, 793

    2008

  8. [16]

    J., Evans K

    Cornwell T. J., Evans K. F., 1985, , https://ui.adsabs.harvard.edu/abs/1985A&A...143...77C 143, 77

    1985

  9. [17]

    B., 1999, in Taylor G

    Cornwell T., Fomalont E. B., 1999, in Taylor G. B., Carilli C. L., Perley R. A., eds, Astronomical Society of the Pacific Conference Series Vol. 180, Synthesis Imaging in Radio Astronomy II. p. 187

    1999

  10. [18]

    Doeleman S., et al., 2009, in astro2010: The Astronomy and Astrophysics Decadal Survey. p. 68 ( @eprint arXiv 0906.3899 ), @doi 10.48550/arXiv.0906.3899

    2009 doi arXiv

  11. [19]

    Event Horizon Telescope Collaboration et al., 2019a, @doi [ ] 10.3847/2041-8213/ab0c96 , https://ui.adsabs.harvard.edu/abs/2019ApJ...875L...2E 875, L2

    doi

  12. [20]

    Event Horizon Telescope Collaboration et al., 2019b, @doi [ ] 10.3847/2041-8213/ab0c57 , https://ui.adsabs.harvard.edu/abs/2019ApJ...875L...3E 875, L3

    doi

  13. [21]

    Event Horizon Telescope Collaboration et al., 2019c, @doi [ ] 10.3847/2041-8213/ab0e85 , https://ui.adsabs.harvard.edu/abs/2019ApJ...875L...4E 875, L4

    doi

  14. [22]

    Event Horizon Telescope Collaboration et al., 2019d, @doi [ ] 10.3847/2041-8213/ab1141 , https://ui.adsabs.harvard.edu/abs/2019ApJ...875L...6E 875, L6

    doi

  15. [23]

    Event Horizon Telescope Collaboration et al., 2022, @doi [ ] 10.3847/2041-8213/ac6429 , https://ui.adsabs.harvard.edu/abs/2022ApJ...930L..14E 930, L14

    2022 doi

  16. [24]

    T., Bouman K

    Feng B. T., Bouman K. L., Freeman W. T., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2406.02785 , https://ui.adsabs.harvard.edu/abs/2024arXiv240602785F p. arXiv:2406.02785

    2024 doi arXiv

  17. [25]

    R., 1972, Journal of the Optical Society of America (1917-1983), https://ui.adsabs.harvard.edu/abs/1972JOSA...62..511F 62, 511

    Frieden B. R., 1972, Journal of the Optical Society of America (1917-1983), https://ui.adsabs.harvard.edu/abs/1972JOSA...62..511F 62, 511

    1972

  18. [26]

    Garsden H., et al., 2015, @doi [ ] 10.1051/0004-6361/201424504 , https://ui.adsabs.harvard.edu/abs/2015A&A...575A..90G 575, A90

    2015 doi

  19. [27]

    E., 2007, @doi [Journal of the Royal Statistical Society: Series B (Statistical Methodology)] https://doi.org/10.1111/j.1467-9868.2007.00587.x , 69, 243

    Gneiting T., Balabdaoui F., Raftery A. E., 2007, @doi [Journal of the Royal Statistical Society: Series B (Statistical Methodology)] https://doi.org/10.1111/j.1467-9868.2007.00587.x , 69, 243

    2007

  20. [28]

    Goddi C., et al., 2019, @doi [ ] 10.1088/1538-3873/ab136a , https://ui.adsabs.harvard.edu/abs/2019PASP..131g5003G 131, 075003

    2019 doi

  21. [29]

    Greve A., et al., 1995, , https://ui.adsabs.harvard.edu/abs/1995A&A...299L..33G 299, L33

    1995

  22. [30]

    F., Daniell G

    Gull S. F., Daniell G. J., 1978, @doi [ ] 10.1038/272686a0 , https://ui.adsabs.harvard.edu/abs/1978Natur.272..686G 272, 686

    1978 doi

  23. [31]

    A ., Schilke P., Menten K., Cesarsky C., Booth R., 2006, @doi [ ] 10.1051/0004-6361:20065420 , https://ui.adsabs.harvard.edu/abs/2006A&A...454L..13G 454, L13

    G \"u sten R., Nyman L. A ., Schilke P., Menten K., Cesarsky C., Booth R., 2006, @doi [ ] 10.1051/0004-6361:20065420 , https://ui.adsabs.harvard.edu/abs/2006A&A...454L..13G 454, L13

    2006 doi

  24. [32]

    Hersbach H., 2000, @doi [Weather and Forecasting] 10.1175/1520-0434(2000)015<0559:DOTCRP>2.0.CO;2 , https://ui.adsabs.harvard.edu/abs/2000WtFor..15..559H 15, 559

    2000 doi

  25. [33]

    Ho P. T. P., Moran J. M., Lo K. Y., 2004, @doi [ ] 10.1086/423245 , https://ui.adsabs.harvard.edu/abs/2004ApJ...616L...1H 616, L1

    2004 doi

  26. [34]

    A., 1974, , https://ui.adsabs.harvard.edu/abs/1974A&AS...15..417H 15, 417

    H \"o gbom J. A., 1974, , https://ui.adsabs.harvard.edu/abs/1974A&AS...15..417H 15, 417

    1974

  27. [35]

    Honma M., Akiyama K., Uemura M., Ikeda S., 2014, @doi [ ] 10.1093/pasj/psu070 , https://ui.adsabs.harvard.edu/abs/2014PASJ...66...95H 66, 95

    2014 doi

  28. [36]

    H., et al., 2010, in Stepp L

    Hughes D. H., et al., 2010, in Stepp L. M., Gilmozzi R., Hall H. J., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 7733, Ground-based and Airborne Telescopes III. p. 773312, @doi 10.1117/12.857974

    2010 doi

  29. [37]

    D., 2007, @doi [Computing in Science and Engineering] 10.1109/MCSE.2007.55 , https://ui.adsabs.harvard.edu/abs/2007CSE.....9...90H 9, 90

    Hunter J. D., 2007, @doi [Computing in Science and Engineering] 10.1109/MCSE.2007.55 , https://ui.adsabs.harvard.edu/abs/2007CSE.....9...90H 9, 90

    2007 doi

  30. [38]

    Ikeda S., Tazaki F., Akiyama K., Hada K., Honma M., 2016, @doi [ ] 10.1093/pasj/psw042 , https://ui.adsabs.harvard.edu/abs/2016PASJ...68...45I 68, 45

    2016 doi

  31. [39]

    Janssen M., et al., 2021, @doi [Nature Astronomy] 10.1038/s41550-021-01417-w , https://ui.adsabs.harvard.edu/abs/2021NatAs...5.1017J 5, 1017

    2021 doi

  32. [40]

    C., 1958, @doi [ ] 10.1093/mnras/118.3.276 , https://ui.adsabs.harvard.edu/abs/1958MNRAS.118..276J 118, 276

    Jennison R. C., 1958, @doi [ ] 10.1093/mnras/118.3.276 , https://ui.adsabs.harvard.edu/abs/1958MNRAS.118..276J 118, 276

    1958 doi

  33. [41]

    10708, Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy IX

    Kim J., et al., 2018, in Zmuidzinas J., Gao J.-R., eds, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series Vol. 10708, Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy IX. p. 107082S ( @eprint arXiv 1805.09346 ), ...

    2018 arXiv

  34. [42]

    Kim J.-Y., et al., 2020, @doi [ ] 10.1051/0004-6361/202037493 , https://ui.adsabs.harvard.edu/abs/2020A&A...640A..69K 640, A69

    2020 doi

  35. [43]

    P., Ba J., 2014, @doi [arXiv e-prints] 10.48550/arXiv.1412.6980 , https://ui.adsabs.harvard.edu/abs/2014arXiv1412.6980K p

    Kingma D. P., Ba J., 2014, @doi [arXiv e-prints] 10.48550/arXiv.1412.6980 , https://ui.adsabs.harvard.edu/abs/2014arXiv1412.6980K p. arXiv:1412.6980

    2014 doi arXiv

  36. [44]

    Kramer M., 1992, @doi [Computers & Chemical Engineering] https://doi.org/10.1016/0098-1354(92)80051-A , 16, 313

    1992 doi

  37. [45]

    University of Toronto, Toronto, Ontario

    Krizhevsky A., 2009, Technical report, Learning multiple layers of features from tiny images. University of Toronto, Toronto, Ontario

    2009

  38. [46]

    L., Pu H.-Y., Asada K., Honma M., 2018, @doi [ ] 10.3847/1538-4357/aab6b5 , https://ui.adsabs.harvard.edu/abs/2018ApJ...858...56K 858, 56

    Kuramochi K., Akiyama K., Ikeda S., Tazaki F., Fish V. L., Pu H.-Y., Asada K., Honma M., 2018, @doi [ ] 10.3847/1538-4357/aab6b5 , https://ui.adsabs.harvard.edu/abs/2018ApJ...858...56K 858, 56

    2018 doi

  39. [47]

    Lai S., 2024, samlaihei/DIReCT: v1.0.0 DIReCT, @doi 10.5281/zenodo.14032844 , https://doi.org/10.5281/zenodo.14032844

    2024 doi

  40. [48]

    J., de Hoog F., 2011, @doi [ ] 10.1051/0004-6361/201015045 , https://ui.adsabs.harvard.edu/abs/2011A&A...528A..31L 528, A31

    Li F., Cornwell T. J., de Hoog F., 2011, @doi [ ] 10.1051/0004-6361/201015045 , https://ui.adsabs.harvard.edu/abs/2011A&A...528A..31L 528, A31

    2011 doi

  41. [49]

    L., Aller M

    Lister M. L., Aller M. F., Aller H. D., Hodge M. A., Homan D. C., Kovalev Y. Y., Pushkarev A. B., Savolainen T., 2018, @doi [ ] 10.3847/1538-4365/aa9c44 , https://ui.adsabs.harvard.edu/abs/2018ApJS..234...12L 234, 12

    2018 doi

  42. [50]

    pp 3730--3738, @doi 10.1109/ICCV.2015.425

    Liu Z., Luo P., Wang X., Tang X., 2015, in 2015 IEEE International Conference on Computer Vision (ICCV). pp 3730--3738, @doi 10.1109/ICCV.2015.425

    2015 doi

  43. [51]

    E., 2022, @doi [ ] 10.1093/mnras/stab3204 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.3643L 509, 3643

    Lockhart W., Gralla S. E., 2022, @doi [ ] 10.1093/mnras/stab3204 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.3643L 509, 3643

    2022 doi

  44. [52]

    A., Richardson J

    Marsh K. A., Richardson J. M., 1987, , https://ui.adsabs.harvard.edu/abs/1987A&A...182..174M 182, 174

    1987

  45. [53]

    Mertens F., Lobanov A., 2015, @doi [ ] 10.1051/0004-6361/201424566 , https://ui.adsabs.harvard.edu/abs/2015A&A...574A..67M 574, A67

    2015 doi

  46. [54]

    arXiv:2407.20190

    M \"u ller H., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2407.20190 , https://ui.adsabs.harvard.edu/abs/2024arXiv240720190M p. arXiv:2407.20190

    2024 doi arXiv

  47. [55]

    P., 2022, @doi [ ] 10.1051/0004-6361/202243244 , https://ui.adsabs.harvard.edu/abs/2022A&A...666A.137M 666, A137

    M \"u ller H., Lobanov A. P., 2022, @doi [ ] 10.1051/0004-6361/202243244 , https://ui.adsabs.harvard.edu/abs/2022A&A...666A.137M 666, A137

    2022 doi

  48. [56]

    M \"u ller H., Mus A., Lobanov A., 2023, @doi [ ] 10.1051/0004-6361/202346207 , https://ui.adsabs.harvard.edu/abs/2023A&A...675A..60M 675, A60

    2023 doi

  49. [57]

    Narayan R., Nityananda R., 1986, @doi [ ] 10.1146/annurev.aa.24.090186.001015 , https://ui.adsabs.harvard.edu/abs/1986ARA&A..24..127N 24, 127

    1986

  50. [58]

    R., et al., 2014, @doi [ ] 10.1093/mnras/stu1368 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.444..606O 444, 606

    Offringa A. R., et al., 2014, @doi [ ] 10.1093/mnras/stu1368 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.444..606O 444, 606

    2014 doi

  51. [59]

    arXiv:1912.01703

    Paszke A., et al., 2019, @doi [arXiv e-prints] 10.48550/arXiv.1912.01703 , https://ui.adsabs.harvard.edu/abs/2019arXiv191201703P p. arXiv:1912.01703

    2019 doi arXiv

  52. [60]

    L., 2017, in Brescia M., Djorgovski S

    Polsterer K. L., 2017, in Brescia M., Djorgovski S. G., Feigelson E. D., Longo G., Cavuoti S., eds, IAU Symposium Vol. 325, Astroinformatics. pp 156--165, @doi 10.1017/S1743921316013089

    2017 doi

  53. [61]

    L., Gieseke F., 2019, in Molinaro M., Shortridge K., Pasian F., eds, Astronomical Society of the Pacific Conference Series Vol

    Polsterer K. L., Gieseke F., 2019, in Molinaro M., Shortridge K., Pasian F., eds, Astronomical Society of the Pacific Conference Series Vol. 521, Astronomical Data Analysis Software and Systems XXVI. p. 240

    2019

  54. [62]

    D., d'Avezac M., Carrillo R

    Pratley L., McEwen J. D., d'Avezac M., Carrillo R. E., Onose A., Wiaux Y., 2018, @doi [ ] 10.1093/mnras/stx2237 , https://ui.adsabs.harvard.edu/abs/2018MNRAS.473.1038P 473, 1038

    2018 doi

  55. [63]

    Readhead A. C. S., Wilkinson P. N., 1978, @doi [ ] 10.1086/156232 , https://ui.adsabs.harvard.edu/abs/1978ApJ...223...25R 223, 25

    1978 doi

  56. [64]

    Roelofs F., et al., 2023, @doi [ ] 10.3847/2041-8213/acff6f , https://ui.adsabs.harvard.edu/abs/2023ApJ...957L..21R 957, L21

    2023 doi

  57. [65]

    Rogers A. E. E., et al., 1974, @doi [ ] 10.1086/153162 , https://ui.adsabs.harvard.edu/abs/1974ApJ...193..293R 193, 293

    1974 doi

  58. [66]

    I., Osher S., Fatemi E., 1992, @doi [Physica D: Nonlinear Phenomena] https://doi.org/10.1016/0167-2789(92)90242-F , 60, 259

    Rudin L. I., Osher S., Fatemi E., 1992, @doi [Physica D: Nonlinear Phenomena] https://doi.org/10.1016/0167-2789(92)90242-F , 60, 259

    1992 doi

  59. [67]

    Samuel J., Nityananda R., Thyagarajan N., 2022, @doi [ ] 10.1103/PhysRevLett.128.091101 , https://ui.adsabs.harvard.edu/abs/2022PhRvL.128i1101S 128, 091101

    2022 doi

  60. [68]

    J., 1978, , https://ui.adsabs.harvard.edu/abs/1978A&A....65..345S 65, 345

    Schwarz U. J., 1978, , https://ui.adsabs.harvard.edu/abs/1978A&A....65..345S 65, 345

    1978

  61. [69]

    Shepherd M., 2011, Difmap: Synthesis Imaging of Visibility Data , Astrophysics Source Code Library, record ascl:1103.001

    2011

  62. [70]

    L., 2020, @doi [arXiv e-prints] 10.48550/arXiv.2010.14462 , https://ui.adsabs.harvard.edu/abs/2020arXiv201014462S p

    Sun H., Bouman K. L., 2020, @doi [arXiv e-prints] 10.48550/arXiv.2010.14462 , https://ui.adsabs.harvard.edu/abs/2020arXiv201014462S p. arXiv:2010.14462

    2020 doi arXiv

  63. [71]

    L., Tiede P., Wang J

    Sun H., Bouman K. L., Tiede P., Wang J. J., Blunt S., Mawet D., 2022, @doi [ ] 10.3847/1538-4357/ac6be9 , https://ui.adsabs.harvard.edu/abs/2022ApJ...932...99S 932, 99

    2022 doi

  64. [72]

    B., Carilli C

    Taylor G. B., Carilli C. L., Perley R. A., eds, 1999, Synthesis Imaging in Radio Astronomy II Astronomical Society of the Pacific Conference Series Vol. 180

    1999

  65. [73]

    R., Moran J

    Thompson A. R., Moran J. M., Swenson George W. J., 2017, Interferometry and Synthesis in Radio Astronomy, 3rd Edition . Astronomy & Astrophysics Library, @doi 10.1007/978-3-319-44431-4

    2017 doi

  66. [74]

    Thyagarajan N., Nityananda R., Samuel J., 2022, @doi [ ] 10.1103/PhysRevD.105.043019 , https://ui.adsabs.harvard.edu/abs/2022PhRvD.105d3019T 105, 043019

    2022 doi

  67. [75]

    I., 2024, @doi [RAS Techniques and Instruments] 10.1093/rasti/rzae031 , https://ui.adsabs.harvard.edu/abs/2024RASTI...3..437T 3, 437

    Thyagarajan N., Hoefs L., Wong O. I., 2024, @doi [RAS Techniques and Instruments] 10.1093/rasti/rzae031 , https://ui.adsabs.harvard.edu/abs/2024RASTI...3..437T 3, 437

    2024 doi

  68. [76]

    Q., Carter A

    Twiss R. Q., Carter A. W. L., Little A. G., 1960, The Observatory, https://ui.adsabs.harvard.edu/abs/1960Obs....80..153T 80, 153

    1960

  69. [77]

    N., Kaiser L., Polosukhin I., 2017, @doi [arXiv e-prints] 10.48550/arXiv.1706.03762 , https://ui.adsabs.harvard.edu/abs/2017arXiv170603762V p

    Vaswani A., Shazeer N., Parmar N., Uszkoreit J., Jones L., Gomez A. N., Kaiser L., Polosukhin I., 2017, @doi [arXiv e-prints] 10.48550/arXiv.1706.03762 , https://ui.adsabs.harvard.edu/abs/2017arXiv170603762V p. arXiv:1706.03762

    2017 doi arXiv

  70. [78]

    Virtanen P., et al., 2020, @doi [Nature Methods] 10.1038/s41592-019-0686-2 , https://ui.adsabs.harvard.edu/abs/2020NatMe..17..261V 17, 261

    2020 doi

  71. [79]

    P., Schwarz U

    Wakker B. P., Schwarz U. J., 1988, , https://ui.adsabs.harvard.edu/abs/1988A&A...200..312W 200, 312

    1988

  72. [80]

    Wiaux Y., Jacques L., Puy G., Scaife A. M. M., Vandergheynst P., 2009, @doi [ ] 10.1111/j.1365-2966.2009.14665.x , https://ui.adsabs.harvard.edu/abs/2009MNRAS.395.1733W 395, 1733

    2009

  73. [81]

    Wielgus M., et al., 2022, @doi [ ] 10.1051/0004-6361/202244493 , https://ui.adsabs.harvard.edu/abs/2022A&A...665L...6W 665, L6

    2022 doi

  74. [82]

    R., 2009, @doi [IEEE Proceedings] 10.1109/JPROC.2009.2020572 , https://ui.adsabs.harvard.edu/abs/2009IEEEP..97.1463W 97, 1463

    Wootten A., Thompson A. R., 2009, @doi [IEEE Proceedings] 10.1109/JPROC.2009.2020572 , https://ui.adsabs.harvard.edu/abs/2009IEEEP..97.1463W 97, 1463

    2009

  75. [83]

    C., Varoquaux G., 2011, @doi [Computing in Science and Engineering] 10.1109/MCSE.2011.37 , https://ui.adsabs.harvard.edu/abs/2011CSE....13b..22V 13, 22

    van der Walt S., Colbert S. C., Varoquaux G., 2011, @doi [Computing in Science and Engineering] 10.1109/MCSE.2011.37 , https://ui.adsabs.harvard.edu/abs/2011CSE....13b..22V 13, 22

    2011 doi

  76. [84]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.