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REVIEW 4 major objections 7 minor 35 references

Deep Image Prior Assisted ISAR Imaging for Missing Data Case

T0 review · 4 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A deep image prior with randomly initialized weights and no training can complete complex ISAR radar echoes even when 70% of samples are missing, outperforming compressive sensing and matrix completion baselines in the paper's experiments.

desk verdict A legitimate new application of DIP to complex ISAR data with broad experiments, but the headline numbers look inflated and the early-stopping rule may leak test information. read the letter →

arxiv 2507.09393 v1 pith:6PGCC2IX submitted 2025-07-12 eess.IV

Necmettin Bayar , Isin Erer , Deniz Kumlu This is my paper · ORCID
classification eess.IV
keywords ISARimagingdeepimagepriormissingdatarecoverymatrixcompletioncompressivesensingcomplex-valueduntrainedneuralnetworksinpainting
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that deep image prior (DIP), a fixed random-weight convolutional network optimized on a single corrupted input, can fill randomly missing entries of complex inverse synthetic aperture radar (ISAR) echo matrices before conventional Fourier imaging. The authors split the complex data into real and imaginary parts, complete each part with an independently initialized DIP network, and recombine them. They compare against three established recovery routes—low-rank matrix completion (IALM and NNM) and 2D compressive sensing (2D-SL0)—on simulated Mig-25 and USS Fletcher targets and on real turntable data of a T-72 tank, under pixel-wise, column-wise, and compressed missing patterns at 30%, 50%, and 70% loss. Their central claim is that DIP is the only method that stays effective at 70% missing data, with quantitative gains they report as up to 100% in RMSE, 50% in correlation, and 30% in image contrast in some extreme cases. If true, this would make training-free deep-network priors a practical alternative for radar data completion where sparsity assumptions fail and low-rank methods break down.

What carries the argument

The load-bearing mechanism is deep image prior (DIP): a randomly initialized encoder-decoder convolutional network with a fixed noise input, optimized by gradient descent so that its output matches the observed entries of the corrupted matrix under an MSE loss. The prior is implicit in the network architecture and initialization; no external training data is used. The paper uses the SkipNet variant, whose gating functions decide whether to skip blocks, with added convolutional layers on skip connections, a depth of six, channel sizes 256–128–64–64–128–256, 5x5 kernels, Swish activation, and Adam at a learning rate of 1e-3, with early stopping based on SNR convergence. The complex ISAR matrix is completed by running two independent such networks on the real and imaginary parts, normalizing inputs to [0,1] and denormalizing outputs before recombination, after which a 2D Fourier transform forms the image.

What would settle it

Take a synthetic complex ISAR matrix whose real and imaginary parts share a known phase structure, drop 70% of its entries, run the proposed real/imaginary DIP completion, and compare the phase of the reconstructed complex matrix against ground truth; if the independent networks introduce different biases, phase error will grow and the final image will show artifacts even when each component's RMSE is low. A simpler version is to report per-component RMSEs alongside the complex-matrix RMSE and check whether the latter is consistent with phase coherence.

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Extended reading notes

Core claim

The paper's central claim is that an untrained convolutional network, optimized on only the observed samples, imposes a natural-image-like prior strong enough to reconstruct missing complex radar data. Because the data term penalizes only known entries, the network fills the missing positions by fitting the observed pattern; the authors show this survives up to 70% random loss of the raw echo matrix, a regime where NNM produces line artifacts and 2D-SL0 corrupts target structure. The method's specific move is to treat the real and imaginary channels as separate grayscale-like completion problems, adding normalization and denormalization to avoid scale loss, and to use a SkipNet architecture with gating-based skip connections and added convolutions on the skip paths. Their experiments report that DIP ranks first on RMSE and correlation in most tested scenarios, and that its performance is nearly flat across missing ratios on real data, while the comparison methods degrade sharply.

Load-bearing premise

The load-bearing premise is that filling the real and imaginary parts separately with two independent networks, then putting them back together, preserves the phase relationship between the components well enough for coherent Fourier imaging; the paper checks this only on its test scenarios, not by measuring phase error directly.

Editorial extensions

If this is right

  • If the central claim is correct, DIP-based completion offers a training-free route to ISAR imaging under severe random data loss, removing the need for sparsity dictionaries or low-rank parameter tuning.
  • The method handles pixel-wise, column-wise, and compressed missing patterns in a single pipeline, so one implementation could replace separate compressive sensing and matrix completion preprocessing chains.
  • Because completion happens in the raw data domain, the completed echo matrix can be followed by any imaging algorithm, not only the range-Doppler method shown.
  • The reported robustness to SNR values between -30 and 30 dB suggests the approach could also serve noisy as well as missing-data scenarios without retraining.

Reading between the lines

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

  • An implicit consequence is that the same real/imaginary split-and-recombine trick might extend to other complex-valued sensor data such as SAR, GPR, or MRI k-space, with the same phase-coherence caveat.
  • The paper does not analyze whether the two independent DIP networks preserve the phase relationship between the real and imaginary parts; a testable extension would be to measure the phase error of the reconstructed complex matrix directly and compare it against a complex-valued DIP variant that couples the channels.
  • If the phase-coherence concern is real, artifacts could be expected specifically where the real and imaginary components share correlated fine structure, a regime the current three-target evaluation may not fully stress.
  • The reported running time of roughly 7 seconds on a 221x79 matrix suggests acceleration or shallower variants would be needed before real-time ISAR use, since the paper states DIP is slower than IALM and 2D-SL0.
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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

4 major / 7 minor

Summary. The paper addresses random missing data in inverse synthetic aperture radar (ISAR) echo matrices by proposing a deep image prior (DIP) based completion method. The complex echo matrix is split into real and imaginary parts, each completed by an independently initialized and normalized DIP network, then recombined and imaged with a conventional Fourier-based range-Doppler method. The method requires no training and uses only the observed entries in the loss. The authors compare DIP against IALM, 2D-SL0, and NNM for pixel-wise, column-wise, and compressed missing patterns at 30%, 50%, and 70% missing ratios, using simulated Mig-25 and USS Fletcher data and real T-72 turntable data. Quantitative comparisons use RMSE, correlation, and image contrast, plus a runtime comparison. The paper claims that DIP remains effective at high missing ratios and reports large percentage improvements in the abstract.

Significance. If the central claim is correct, the paper offers a training-free alternative to compressive sensing and matrix completion for ISAR with severe data loss, avoiding dictionary construction and low-rank assumptions. The experimental design is broad: three missing scenarios, three missing ratios, two simulated datasets, and one real dataset, with both visual and quantitative comparisons. The paper also includes a runtime comparison and a noise robustness experiment. However, the lack of a defined stopping rule, single-run results without seeds or error bars, and unsupported abstract percentages currently prevent the claim from being accepted at face value. The contribution is promising but requires a fairer experimental protocol and reproducibility details.

major comments (4)
  1. [5.4 and Fig. 19] The early-stopping criterion for DIP is not reproducible because SNR is never defined and no reference is stated. Since the authors generate masks from complete data, the natural reading of Fig. 19 is that SNR is computed against the original full-data image; if so, DIP is stopped using test labels, whereas IALM, 2D-SL0, and NNM are stopped by fixed tolerance (1e-5) and an iteration cap. This makes the comparison unfair and the claim in Section 5.1 that 'the proposed DIP is the only method that remains effective at a 70% missing ratio' potentially an artifact of oracle stopping. Please define SNR, state its reference, and either use a stopping rule based only on observed entries (e.g., validation loss on a held-out subset of the observed data) or give the baselines the same oracle stopping and show that the conclusions are unchanged.
  2. [Tables 1-10] All quantitative results are reported as single numbers for each configuration, yet DIP is stochastic: Section 4 states that the network parameters are initialized randomly, and the masks are also randomly generated. A single favorable initialization or mask can dominate the reported advantage at 70% missing ratio. Please report means and standard deviations over multiple random seeds and masks (at least 5-10 runs per setting), state the seeds, and make code and data available so the results can be reproduced.
  3. [Abstract and Section 5.1] The abstract's quantitative claims are not supported by the tables. For example, Table 1 at 70% missing ratio gives DIP RMSE 0.3139 versus IALM 0.5817, a relative reduction of about 46%, not the '100% increase' stated in the abstract; correlation at 70% in Table 1 goes from 0.8430 (IALM) to 0.9447 (DIP), about a 12% relative improvement, not 50%. Moreover, the phrase 'only method that remains effective at a 70% missing ratio' is scenario-specific: in the real-data pixel-wise 70% case (Table 8), IALM and NNM also achieve correlation above 0.98. Please re-state the headline claims using the actual table values and clearly scope them to the specific dataset and scenario.
  4. [4, Eq. (13), and Fig. 5] The proposed method completes the real and imaginary parts with independently initialized and independently normalized DIP networks and then recombines them. The paper does not analyze whether independent completion preserves the phase relationship between the two components; different biases in the two reconstructions can produce Fourier-domain artifacts even when each component has low RMSE. This is a load-bearing assumption for the imaging claim. Please add a complex-domain evaluation (e.g., phase error or complex RMSE of the completed echo matrix before imaging) and discuss or test the sensitivity of the final image to the independent-component design.
minor comments (7)
  1. [2, Eq. (4)] Equation (4) has a dimensional inconsistency: the exponentials contain c (speed of light) in the denominator, which cannot cancel to produce the dimensionless phase in a 2D DFT; please correct the derivation and align it with the resolution definitions Δy=c/(2NΔf) and Δx=c/(2MΔθ).
  2. [5.2 and Table 7] The data details are referred to as 'Table??' in Section 5.2, and the compressed-case real data discussion says 'it can be seen on Table 6' but should refer to Table 10; please fix these cross-references.
  3. [Tables 1-10] The number of decimal places is inconsistent across entries (e.g., Table 2 reports 0.18427 and 0.35286 while neighboring entries have four decimals); please unify formatting.
  4. [5.1 and figure captions] The acronym 'RD' is used for the imaging result (e.g., Fig. 6(a)) but is never expanded; please define 'range-Doppler' at first use.
  5. [5.3] The noise experiment does not define how SNR is computed, what quantity is plotted in Fig. 18, or whether noise is added to the full data before masking; please specify these details.
  6. [4] Equation (13) uses the same norm notation for the DIP reconstruction operator and for norms, which is confusing; please introduce a dedicated notation for the reconstruction mapping.
  7. [4] The hyperparameters (depth 6, channel sizes 256,128,64,64,128,256, 5x5 kernels, Swish, learning rate 1e-3) are stated as choices but no sensitivity analysis or a priori justification is given; a brief ablation or a statement that these were fixed in advance would strengthen the generalization claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DIP-based ISAR completion is an empirical comparison against external baselines and does not reduce to its inputs by construction.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The signal model in Section 2 is a standard far-field ISAR formulation, and the DIP formulation in Section 4 is the standard deep image prior inpainting setup: the loss in Eq. (9) is computed only over the observed entries, and the network is optimized to match those entries without ever being fit to the final image-quality metric or to the claimed advantage. The real/imaginary decomposition is a processing choice for handling complex data, not a definition that encodes the reported outcome. Quantitative claims are obtained by comparing reconstructed images with original images using external baselines (IALM, 2D-SL0, NNM) on simulated and real data, so the reported RMSE, Correlation, and IC improvements are not fitted parameters renamed as predictions. The self-citations [21] and [26] provide background and motivation from the same authors' earlier work on GPR and matrix completion, but they are not load-bearing evidence for the ISAR-specific results; the DIP method and its evaluation are presented directly in this paper. Concerns about undefined SNR-based early stopping or single-realization tables would be reproducibility or experimental-fairness issues, not circular reductions by construction, and the paper's own equations do not make any claimed prediction equivalent to its inputs.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on five domain or hand-crafted assumptions and on a set of hand-tuned hyperparameters; there are no invented physical entities.

free parameters (6)
  • DIP network depth = 6
    Set by hand; deeper networks increase cost, shallower reduce accuracy (Section 4).
  • DIP channel sizes = 256,128,64,64,128,256
    Chosen after experiments showing performance peaks then declines with channel size (Section 4).
  • Convolution kernel size = 5x5
    Selected for reconstruction experiments (Section 4).
  • Activation function = Swish
    Best results obtained with Swish, so it is used (Section 4).
  • Learning rate = 1e-3
    Adam optimizer learning rate (Section 4).
  • Early stopping criterion = 3 consecutive iterations with <=1% SNR improvement
    Defined in Section 5.4 to terminate training.
assumptions (5)
  • domain assumption The ISAR signal follows the far-field, small-angle, point-scatterer model of Eq. (1)-(4)
    Used throughout Section 2 to justify 2D Fourier imaging.
  • domain assumption DIP's convolutional architecture provides a useful implicit prior for complex radar echo matrices
    The core premise of the method; no theoretical justification, only experimental evidence (Section 4).
  • ad hoc to paper Real and imaginary parts of the complex ISAR data can be completed independently and then recombined without significant phase distortion
    The method's design splits the data; no phase-error analysis is given.
  • domain assumption The observed entries of the data matrix are accurate and the mask is known
    The loss in Eq. (9) uses only observed entries; measurement noise is considered only in Section 5.3.
  • ad hoc to paper The hyperparameters chosen (depth, channels, activation) generalize across datasets
    The same network settings are used for all datasets; no validation split is described.

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Cite this review

Pith. "Pith review of Deep Image Prior Assisted ISAR Imaging for Missing Data Case." pith.science (2026). https://pith.science/paper/6PGCC2IX

@misc{pith2026250709393,
  author       = {Pith},
  title        = {Pith review of: Deep Image Prior Assisted ISAR Imaging for Missing Data Case},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6PGCC2IX}},
  note         = {Machine review of arXiv:2507.09393}
}
read the original abstract

In Inverse Synthetic Aperture Radar (ISAR), random missing entries of the received radar echo matrix deteriorate the imaging quality, compromising target distinction from the background. Compressive sensing techniques or matrix completion prior to conventional imaging have been used in recent years to solve this issue. However, while the former techniques fail to preserve target continuity due to the sparsity constraint, the latter fails for high missing ratios. This paper proposes to use deep image prior (DIP) to complete the complex radar data and then obtain the radar image by conventional Fourier imaging. Real and imaginary parts are separately completed by independent deep structures and then put together for the imaging part. The proposed DIP based imaging method has been compared with IALM, 2D-SL0 and NNM methods visually and quantitatively for both simulated and real data. The results demonstrate an increase of 100% for some extreme cases in terms of RMSE, 50% increase on Correlation and 30% increase on IC metrics quantitatively.

Figures

Figures reproduced from arXiv: 2507.09393 by the authors.

Figure 1
Figure 1. ISAR geometry representation. where R0 is the range from radar to the origin and ω is the angular rotational speed thus ωt corresponds to rotation angle at time t. For stepped frequency radar, radar trans￾mits N pulses with f0 as the initial frequency and ∆f as the frequency step size. As a same way of frequency, angle between radar to target is also changed with angular step of radar. So fn = f0 + (n − 1)∆f and θm … view at source ↗
Figure 2
Figure 2. Missing Data recovery steps of DIP method. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. SkipNet Architecture that is embedded into DIP [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: Layers of the DIP network with skip connections. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Flow diagram of Proposed Method. and best results are obtained with Swish thus, it is used as activation function. Adam optimizer is used with learning rate as 1e-3 and MSE as loss function. As it is previously noted, model depth is set as six and channel sizes are set…
Figure 6
Figure 6. Figure 6: (a) ISAR imaging result of simulated Mig-25 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: (a) ISAR imaging result of simulated USS [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Visual comparison of ISAR imaging completion methods for simulated Mig-25. The pixel-wise missing rates [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Visual comparison of ISAR imaging completion methods for simulated Mig-25. The missing column rates [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: Visual comparison of ISAR imaging completion methods for simulated Mig-25. The compressed rates (%) [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: Visual comparison of ISAR imaging completion methods for simulated Uss Fletcher warship. The pixel [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 12
Figure 12. Figure 12: Visual comparison of ISAR imaging completion methods for simulated Uss Fletcher warship. The column [PITH_FULL_IMAGE:figures/full_fig_p011_12.png]
Figure 13
Figure 13. Figure 13: Visual comparison of ISAR imaging completion methods for simulated Uss Fletcher warship. The [PITH_FULL_IMAGE:figures/full_fig_p011_13.png]
Figure 14
Figure 14. Figure 14: (a) ISAR imaging result of real T-72 Tank with full data by using RD algorithm. ISAR image is normalized [PITH_FULL_IMAGE:figures/full_fig_p012_14.png]
Figure 15
Figure 15. Figure 15: Visual comparison of ISAR imaging completion methods for real T-72 tank. The pixel-wise missing rates [PITH_FULL_IMAGE:figures/full_fig_p013_15.png]
Figure 16
Figure 16. Figure 16: Visual comparison of ISAR imaging completion methods for real T-72 tank. The column-wise missing rates [PITH_FULL_IMAGE:figures/full_fig_p013_16.png]
Figure 17
Figure 17. Figure 17: Visual comparison of ISAR imaging completion methods for real T-72 tank. The compressed rates (%) are: [PITH_FULL_IMAGE:figures/full_fig_p015_17.png]
Figure 18
Figure 18. Figure 18: SNR of the imaging results in different noise [PITH_FULL_IMAGE:figures/full_fig_p015_18.png]
Figure 19
Figure 19. Figure 19: An example speed test of proposed model for [PITH_FULL_IMAGE:figures/full_fig_p016_19.png]

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Reviewed August 6, 2026 · model on record in the stance chip above.