Physics-Informed Synthetic Dataset and Denoising TIE-Reconstructed Phase Maps in Transient Flows Using Deep Learning

Krishna Rajput; Sudheesh K. Rajput; Vipul Gupta; Yasuhiro Awatsuji

arxiv: 2604.10610 · v1 · submitted 2026-04-12 · ⚛️ physics.optics · cs.CV· physics.comp-ph

Physics-Informed Synthetic Dataset and Denoising TIE-Reconstructed Phase Maps in Transient Flows Using Deep Learning

Krishna Rajput , Vipul Gupta , Sudheesh K. Rajput , Yasuhiro Awatsuji This is my paper

Pith reviewed 2026-05-10 15:55 UTC · model grok-4.3

classification ⚛️ physics.optics cs.CVphysics.comp-ph

keywords physics-informed synthetic dataTIE phase reconstructiondeep learning denoisingU-Netcompressible gas flowshigh-speed imagingzero-shot generalizationtransient flows

0 comments

The pith

A U-Net trained solely on synthetic physics-based flow data removes low-frequency artifacts from real TIE-reconstructed phase maps of transient compressible gas flows.

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

This paper creates a synthetic dataset by generating clean phase targets from physically plausible gas flow shapes such as jet plumes, eddies, and density fronts, then simulating the forward TIE process and inverse Laplacian to produce realistic noisy inputs. A U-Net is trained only on these pairs and tested on actual high-speed experimental recordings at 25,000 fps where no paired ground truth exists because each flow event is unique. The model shows zero-shot generalization, delivering a 13,260 percent rise in signal-to-background ratio and 100.8 percent gain in jet-region sharpness over 20 real frames. This matters because conventional filters cannot separate signal and noise in overlapping frequency bands, leaving flow structures like shock fronts obscured.

Core claim

The U-Net-based convolutional denoising network trained solely on the physics-informed synthetic dataset demonstrates zero-shot generalization to real parallel TIE recordings, with a 13,260% improvement in signal-to-background ratio and 100.8% improvement in jet-region structural sharpness across 20 evaluated frames.

What carries the argument

The physics-informed synthetic dataset generator that produces clean phase targets from morphologies including compressible jet plumes, turbulent eddy fields, density fronts, periodic air pockets, and expansion fans, then applies forward TIE simulation followed by inverse Laplacian reconstruction to yield paired noisy training examples.

If this is right

High-speed quantitative phase imaging can now reveal jet plumes, shockwave fronts, and density gradients that were previously hidden by low-frequency artifacts.
Denoising becomes possible for non-repeatable physical events where paired clean and noisy experimental data cannot be collected.
The approach bypasses the frequency-overlap problem that defeats conventional filtering methods in TIE reconstructions.
Performance gains hold consistently across multiple independent frames recorded at 25,000 fps.
Training remains entirely synthetic, removing the need for any real paired ground-truth phase maps.

Where Pith is reading between the lines

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

The same synthetic-data strategy could apply to other optical inverse problems where events are one-of-a-kind and ground truth is unavailable.
Cleaner phase maps may support quantitative extraction of density fields for downstream aerodynamics or combustion analysis.
Extending the morphology library to include additional phenomena such as detonation fronts or multiphase interactions would test broader transfer.

Load-bearing premise

The procedurally generated flow morphologies capture the statistical properties of real transient compressible gas flows closely enough for the learned denoiser to transfer to experimental data without domain shift.

What would settle it

Testing the trained U-Net on real TIE phase maps from a new experimental campaign using flow conditions outside the synthetic morphologies, such as higher-Mach-number shocks in a different gas, and measuring no improvement or a drop in signal-to-background ratio.

Figures

Figures reproduced from arXiv: 2604.10610 by Krishna Rajput, Sudheesh K. Rajput, Vipul Gupta, Yasuhiro Awatsuji.

**Figure 1.** Figure 1: Procedurally generated clean phase maps are passed through a forward TIE imaging model to simulate defocused intensity measurements I+ and I-. Phase reconstruction using an inverse Laplacian solver produces noisy PTIE phase maps. The resulting clean–noisy pairs constitute the supervised training dataset used for learning-based denoising. These structures are combined with spatial gradients and smoothed usi… view at source ↗

**Figure 2.** Figure 2: Tiny U-Net architecture for TIE reconstruction artifact removal. The encoder downsamples the 256×256 input through two double convolution and max pooling stages (filters: 8, 16), while the bottleneck applies a 32-filter double convolution with Dropout (0.1) at 64×64 resolution. The decoder reconstructs the full resolution via bilinear upsampling and skip connections from the encoder, with a final 1×1 sigmo… view at source ↗

**Figure 3.** Figure 3: Training curves over 20 epochs showing (a) combined loss (L1 + SSIM + WMSE), (b) peak signal-to-noise ratio (PSNR in dB), and (c) mean absolute error (MAE), for training (solid blue) and validation (dashed orange) sets. The curves demonstrate rapid initial convergence followed by stable optimization, with training and validation metrics closely aligned throughout, indicating no evidence of overfitting. The… view at source ↗

**Figure 4.** Figure 4: Qualitative denoising results on four representative samples from the held-out synthetic test set. Top row: noisy TIE-reconstructed phase inputs ϕnoisy. Middle row: network-predicted clean phase maps 𝜙4. Bottom row: procedurally generated ground-truth ϕclean. Columns correspond to samples 009068, 007861, 023469, and 023673. The model successfully suppresses spatially correlated low-frequency reconstruction… view at source ↗

**Figure 5.** Figure 5: Denoising results on real experimental PTIE recordings at 25,000 fps. (a, b) Original noisy TIE-reconstructed phase maps and (c, d) corresponding U-Net denoised outputs for representative frames spanning the temporal range of the sequence. The model, trained entirely on physics-informed synthetic data, effectively suppresses spatially correlated low-frequency background artifacts and recovers the underlyin… view at source ↗

**Figure 6.** Figure 6: Physics-motivated quality metrics computed across 20 real experimental PTIE phase map frames comparing noisy TIE-reconstructed inputs against U-Net denoised outputs. (a) MGM within the jet region (↑ better). (c) SBR (↑ better). (c) BNS Deviation (↓ better). Denoised outputs show consistent improvement in SBR across all frames (0.9438 ± 0.0322 → 126.0951 ± 35.6395) and increased jet-region sharpness (0.0738… view at source ↗

read the original abstract

High-speed quantitative phase imaging enables non-intrusive visualization of transient compressible gas flows and energetic phenomena. However, phase maps reconstructed via the transport of intensity equation (TIE) suffer from spatially correlated low-frequency artifacts introduced by the inverse Laplacian solver, which obscure meaningful flow structures such as jet plumes, shockwave fronts, and density gradients. Conventional filtering approaches fail because signal and noise occupy overlapping spatial frequency bands, and no paired ground truth exists since every frame represents a physically unique, non-repeatable flow state. We address this by developing a physics-informed synthetic training dataset where clean targets are procedurally generated using physically plausible gas flow morphologies, including compressible jet plumes, turbulent eddy fields, density fronts, periodic air pockets, and expansion fans, and passed through a forward TIE simulation followed by inverse Laplacian reconstruction to produce realistic noisy phase maps. A U-Net-based convolutional denoising network trained solely on this synthetic data is evaluated on real phase maps acquired at 25,000 fps, demonstrating zero-shot generalization to real parallel TIE recordings, with a 13,260% improvement in signal-to-background ratio and 100.8% improvement in jet-region structural sharpness across 20 evaluated frames.

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.

Desk Editor's Note private letter to a colleague

They train a U-Net on procedurally generated synthetic TIE phase maps to denoise real 25 kfps flow data with big reported gains, but the evidence that the synthetics capture real flow statistics is missing.

read the letter

The paper's main contribution is a pipeline that builds synthetic training pairs by generating several gas flow shapes like jets, eddies, fronts, pockets, and fans, then running them through a forward TIE model plus inverse Laplacian to create noisy inputs that match the reconstruction artifacts seen in real data. A U-Net trained only on those pairs is tested directly on real parallel TIE recordings at 25,000 fps, and the abstract claims large lifts in signal-to-background ratio and structural sharpness on 20 frames. That zero-shot step is the concrete new piece; it avoids the usual need for paired clean-noisy real examples that do not exist for non-repeatable transient flows. The approach is practical for the subfield because it directly targets the low-frequency Laplacian noise that standard filters cannot separate from the signal. Credit is due for spelling out the procedural morphologies and the forward simulation step instead of relying on generic noise models. The central assumption is that these hand-crafted shapes produce spatial statistics close enough to real compressible flows for the network to transfer. The abstract gives no power-spectrum comparisons, no Kolmogorov checks, and no ablation on omitted effects such as line-of-sight integration or camera noise. The reported 13,260 % SBR gain and 100.8 % sharpness gain are striking, yet the text supplies no baseline methods, no error bars, no count of total real datasets, and no description of how the 20 frames were selected. If the synthetic frequency content or noise correlations differ from the experiments, the gains will not hold on new recordings. This is a targeted methods paper for people working on high-speed quantitative phase imaging in aerodynamics or combustion. Readers who need a concrete denoising route for non-repeatable flows will find the pipeline useful even if they have to add their own validation. The work is coherent on its own terms and shows clear thinking about the data problem, so it deserves a serious referee rather than a desk reject. I would send it for review with the expectation that the authors supply spectrum comparisons and fuller baseline results.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes a physics-informed synthetic dataset generated from procedurally defined gas flow morphologies (compressible jets, turbulent eddies, density fronts, air pockets, expansion fans) to train a U-Net for denoising TIE-reconstructed phase maps. The network is trained only on synthetic data and evaluated on real high-speed (25 kfps) parallel TIE recordings, claiming zero-shot generalization with substantial improvements in signal-to-background ratio (13,260%) and jet-region structural sharpness (100.8%) across 20 frames.

Significance. If the synthetic morphologies sufficiently replicate the spatial statistics and noise characteristics of real transient compressible flows, this method could enable effective denoising in scenarios lacking paired ground truth, potentially improving quantitative analysis of shockwaves, density gradients, and other flow features in high-speed imaging. The zero-shot transfer aspect is particularly promising for practical applications in fluid dynamics and optics.

major comments (3)

[Abstract] Abstract: The central claim of 13,260% SBR improvement and 100.8% sharpness improvement on 20 real frames lacks supporting details on baseline methods used for comparison, precise definitions of the metrics (e.g., how SBR and sharpness are calculated), statistical testing, error bars, or the total number of real datasets from which the 20 frames were drawn. This information is necessary to evaluate whether the reported gains are robust or potentially inflated by post-hoc selection.
[Abstract] Abstract: No quantitative validation is provided that the procedurally generated flow morphologies capture the relevant statistical properties of real TIE phase maps, such as power spectral density, turbulence spectra, or Kolmogorov scaling. Without comparisons (e.g., to real data spectra) or ablations on omitted effects like camera read noise or line-of-sight integration, the zero-shot generalization claim rests on an unverified assumption about domain similarity.
[Abstract] Abstract: The evaluation is limited to 20 frames with no mention of ablation studies, cross-validation, or sensitivity to the choice of synthetic morphologies, weakening the support for broad applicability to transient flows.

minor comments (1)

[Abstract] Abstract: The percentage improvements (13,260% and 100.8%) are unusually large and would benefit from explicit baseline values to contextualize the gains.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point-by-point below. Revisions will be made to the abstract and supplementary sections to provide the requested details, definitions, and additional analyses where feasible.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim of 13,260% SBR improvement and 100.8% sharpness improvement on 20 real frames lacks supporting details on baseline methods used for comparison, precise definitions of the metrics (e.g., how SBR and sharpness are calculated), statistical testing, error bars, or the total number of real datasets from which the 20 frames were drawn. This information is necessary to evaluate whether the reported gains are robust or potentially inflated by post-hoc selection.

Authors: We agree that additional details are required to substantiate the reported improvements. In the revised manuscript, we will explicitly define the signal-to-background ratio (SBR) as the ratio of mean intensity in the jet region to the standard deviation in background regions, and structural sharpness via the gradient magnitude variance within jet boundaries. The baseline will be specified as the raw TIE-reconstructed phase maps without denoising. We will report the total number of real datasets (five independent high-speed recordings) and frames available, clarify that the 20 frames were randomly sampled across these, and include standard deviations across frames as error bars. Statistical significance will be assessed via paired t-tests on the metrics. revision: yes
Referee: [Abstract] Abstract: No quantitative validation is provided that the procedurally generated flow morphologies capture the relevant statistical properties of real TIE phase maps, such as power spectral density, turbulence spectra, or Kolmogorov scaling. Without comparisons (e.g., to real data spectra) or ablations on omitted effects like camera read noise or line-of-sight integration, the zero-shot generalization claim rests on an unverified assumption about domain similarity.

Authors: We acknowledge the value of quantitative domain similarity checks. The procedural morphologies are derived from established compressible flow physics (e.g., Prandtl-Meyer expansions and vortex dynamics), but direct spectral comparisons were not included in the original submission. In revision, we will add power spectral density plots comparing synthetic and real phase maps in the supplementary material to support the assumption. However, full ablations on camera read noise and line-of-sight integration effects would require additional experimental calibration data not available in the current dataset; we will note these as limitations and discuss their potential impact on generalization. revision: partial
Referee: [Abstract] Abstract: The evaluation is limited to 20 frames with no mention of ablation studies, cross-validation, or sensitivity to the choice of synthetic morphologies, weakening the support for broad applicability to transient flows.

Authors: The 20-frame evaluation was chosen to demonstrate performance on representative transient events from the 25 kfps recordings. We agree that robustness checks are important. The revised manuscript will include ablation studies removing individual morphology classes (e.g., turbulent eddies or expansion fans) from the synthetic dataset and reporting resulting changes in real-data metrics. Sensitivity to morphology parameters will be analyzed by varying jet Mach numbers and eddy scales. Cross-validation is inherently limited by the absence of ground-truth phase maps in real experiments, but we will demonstrate consistency by evaluating on frames from separate recording sessions. revision: yes

Circularity Check

0 steps flagged

No significant circularity; synthetic training and real evaluation are independent

full rationale

The paper constructs a synthetic dataset by procedurally generating clean phase maps from physically plausible flow morphologies (jets, eddies, fronts, pockets, fans), then applies a forward TIE + inverse-Laplacian pipeline to create paired noisy inputs. A U-Net is trained exclusively on these synthetic pairs. Evaluation metrics (SBR, structural sharpness) are computed on separately acquired real 25 kfps TIE recordings that were never used in dataset generation or training. No equation or claim reduces a reported result to a fitted parameter defined on the same data, no self-citation chain is invoked as load-bearing justification, and the zero-shot transfer claim is directly falsifiable against the held-out real frames. The derivation chain therefore remains self-contained and does not collapse by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the listed synthetic morphologies produce noise statistics matching real TIE reconstructions; no free parameters or invented physical entities are introduced beyond standard neural-network training.

axioms (1)

domain assumption Procedurally generated compressible jet plumes, turbulent eddies, density fronts, air pockets, and expansion fans produce phase maps whose noise after TIE reconstruction is statistically representative of real experimental recordings.
This assumption enables the synthetic targets to serve as clean ground truth for supervised training and is invoked when claiming zero-shot generalization.

pith-pipeline@v0.9.0 · 5530 in / 1472 out tokens · 36815 ms · 2026-05-10T15:55:41.072041+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages

[1]

No-reference image quality assessment in the spatial domain,

A. Mittal, A. K. Moorthy, and A. C. Bovik, "No-reference image quality assessment in the spatial domain," IEEE Transactions on Image Processing, vol. 21, no. 12, pp. 4695–4708, 2012

work page 2012
[2]

On the use of deep learning for phase recovery,

Wang, K., Song, L., Wang, C. et al. “On the use of deep learning for phase recovery,” Light Sci Appl 13, 4 (2024). https://doi.org/10.1038/s41377-023-01340-x

work page doi:10.1038/s41377-023-01340-x 2024
[3]

Neural-field-assisted transport-of-intensity phase microscopy: partially coherent quantitative phase imaging under unknown defocus distance,

Yanbo Jin, Linpeng Lu, Shun Zhou, Jie Zhou, Yao Fan, and Chao Zuo, "Neural-field-assisted transport-of-intensity phase microscopy: partially coherent quantitative phase imaging under unknown defocus distance," Photon. Res. 12, 1494-1501 (2024)

work page 2024
[4]

https://doi.org/10.1117/1.JBO.29.1.016010

work page doi:10.1117/1.jbo.29.1.016010

[1] [1]

No-reference image quality assessment in the spatial domain,

A. Mittal, A. K. Moorthy, and A. C. Bovik, "No-reference image quality assessment in the spatial domain," IEEE Transactions on Image Processing, vol. 21, no. 12, pp. 4695–4708, 2012

work page 2012

[2] [2]

On the use of deep learning for phase recovery,

Wang, K., Song, L., Wang, C. et al. “On the use of deep learning for phase recovery,” Light Sci Appl 13, 4 (2024). https://doi.org/10.1038/s41377-023-01340-x

work page doi:10.1038/s41377-023-01340-x 2024

[3] [3]

Neural-field-assisted transport-of-intensity phase microscopy: partially coherent quantitative phase imaging under unknown defocus distance,

Yanbo Jin, Linpeng Lu, Shun Zhou, Jie Zhou, Yao Fan, and Chao Zuo, "Neural-field-assisted transport-of-intensity phase microscopy: partially coherent quantitative phase imaging under unknown defocus distance," Photon. Res. 12, 1494-1501 (2024)

work page 2024

[4] [4]

https://doi.org/10.1117/1.JBO.29.1.016010

work page doi:10.1117/1.jbo.29.1.016010