Freqformer: Image-Demoir\'eing Transformer via Efficient Frequency Decomposition

Bolin Qiu; Jiezhang Cao; Xiaokang Yang; Xiaoyang Liu; Yulun Zhang; Zheng Chen

REVIEW 4 major objections 5 minor 48 references

Freqformer: Image-Demoir\'eing Transformer via Efficient Frequency Decomposition

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A dual-branch Transformer that splits moiré into high-frequency texture and low-frequency color can beat larger demoiréing networks on FHDMi and UHDM.

desk verdict A novel, compact demoiréing transformer with credible SOTA results, undermined by an undocumented scale-robustness claim and a training/inference contradiction. read the letter →

arxiv 2505.19120 v1 pith:6OTWOZFA submitted 2025-05-25 cs.CV

Xiaoyang Liu , Bolin Qiu , Jiezhang Cao , Zheng Chen , Yulun Zhang , Xiaokang Yang This is my paper · ORCID

classification cs.CV

keywords imagedemoiréingfrequencydecompositiondual-branchtransformerlow-frequencycolordistortionhigh-frequencytexturechannelattentionrestorationFHDMi

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

Freqformer argues that moiré artifacts split cleanly by frequency: high-frequency components carry localized texture corruption, low-frequency components carry smooth color distortions. The paper builds a dual-branch Transformer that trains on these two components separately, using random crops for the high-frequency branch and heavily downsampled images for the low-frequency branch, then fuses the branches with a learnable Frequency Composition Transform. On the FHDMi and UHDM benchmarks, Freqformer reports the best PSNR, SSIM, and LPIPS on FHDMi and best SSIM/LPIPS on UHDM, with 6.065M parameters, smaller than most compared models. The paper's point is that explicit frequency separation, not a monolithic mapper, is what makes efficient high-resolution demoiréing feasible.

What carries the argument

The load-bearing object is the recursive frequency decomposition of Eq. (2): starting with $I_l^0 = I_m$, each level applies a dilated 3x3 convolution with the binomial kernel $k$ to get $I_l^i$, and defines the high-frequency residual as $I_h^i = I_h^{i-1} + I_l^{i-1} - I_l^i$. After $L$ levels, $I_l$ is the smooth color component and $I_h$ the texture component, both at full resolution. This decomposition does the work of making the two branches trainable with different strategies, and it feeds the learnable FCT, which combines the branch features before the final PixelShuffle reconstruction.

What would settle it

Take a diverse set of FHDMi and UHDM moiré images, apply the paper's L-level decomposition, downsample the low-frequency component to 0.1x, resize it back, and measure reconstruction PSNR against the original low-frequency component. If typical values fall well below roughly 50 dB, or if images with strong low-frequency scene texture break the scale-robustness, the resize-based training strategy degrades and the dual-branch design loses its justification.

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Extended reading notes

Core claim

The paper claims that the right decomposition of a moiré image is into a low-frequency image that keeps color information and is robust to downsampling, and a high-frequency residual that keeps texture and is spatially local. This decomposition, built from L-level dilated convolutions with a fixed binomial kernel, separates moiré into components with different training needs: crop-based training for the high-frequency branch and resize-based training for the low-frequency branch. A learnable FCT then fuses the two branches in feature space instead of adding pixel outputs, which avoids accumulating reconstruction errors. With this design and a lightweight Spatial-Aware Channel Attention module, the paper reports results on FHDMi and UHDM that beat prior demoiréing and general restoration models, including much larger ones, at 6.065M parameters.

Load-bearing premise

The method assumes the low-frequency component can be downsampled to about one-tenth its size and resized back with roughly 50 dB PSNR, so training on resized low-frequency images is equivalent to training on full-resolution inputs; this is supported only by a one-sentence experiment without protocol details.

Editorial extensions

If this is right

If the decomposition claim is right, demoiréing can be solved by two smaller specialized networks rather than one large holistic network.
Resize-based low-frequency training means the color-correction branch can run at low resolution during training without hurting final quality, cutting memory and compute on 4K inputs.
The learnable FCT removes the need for a fixed inverse transform, so frequency fusion can be tuned to the data instead of being tied to Haar or other predefined wavelets.
The branch-level results in the paper (low branch 29.90 PSNR, high branch 29.20) suggest each branch is independently strong, so the gains are not just from the fusion module.

Reading between the lines

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

The scale-robust low-frequency assumption, if it generalizes, implies that any global color correction task (white balance, tint removal, cross-ISP color shifts) could be trained on downsampled images and then applied at full resolution with the same network.
The decomposition may transfer to other screen-capture artifacts such as flicker banding or subpixel aliasing, since those also have a smooth color component and a local texture component.
A testable extension would be to measure how far the resize factor can be pushed (0.05x, 0.02x) before the roughly 50 dB reconstruction PSNR of the low-frequency branch degrades, giving a direct compute-versus-quality trade-off for 8K inputs.
The paper compares against the 2-level Haar transform and reports a large drop (test PSNR 13.32), but it does not sweep the kernel or level count; varying those could reveal how much of the gain comes from this specific decomposition design.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is worth reading: it introduces a recursive convolution-based frequency split for demoiréing, trains the low-frequency branch on downsampled images, and reports SOTA on FHDMi and UHDM with a 6M-parameter model and public code. The central idea is fresh relative to the wavelet-based prior work (WDNet, AWUDN, MBWDN), and the ablations make a coherent case that resize-based training helps the low branch (Table 3) and that the learnable FCT adds a little. The numbers are plausible, and the code release means the results can be checked.

The soft spots are real but mostly fixable. The load-bearing claim that the low-frequency component is scale-robust—downsampled to 0.1x with ~50 dB reconstruction—is asserted without protocol: the decomposition level L is never given, and the interpolation method, dataset, subset size, and variance are absent. The stress-test worry is right: if L is small, the low-frequency image still contains energy above the 0.1x Nyquist rate, and resizing destroys it. Table 3 gives indirect support, but it doesn't isolate the premise. Also, Sec. 3 says both branches operate at full resolution at test, while Sec. 3.2 bullet 4 says the low branch uses the same small scale at training and inference; that contradiction needs resolving. The Haar baseline (PSNR 13.32, SSIM 0.2113) is implausibly bad—worse than the input—which suggests the newly trained Haar model may be broken or the training setup is unfair; a comparison against an existing wavelet method like WDNet would be more informative. No error bars anywhere.

These issues don't sink the central claim, but they need to be answered. A referee should ask for the decomposition level and a full protocol for the 0.1x experiment, clarify the test-time pipeline, and rerun the Haar ablation with a proper baseline. The paper deserves peer review, not desk rejection, because the method is novel, the results are measurable, and the code is public. If I worked on demoiréing I'd cite it after the revision. I'd maybe bring it to reading group to discuss the decomposition.

Referee Report

4 major / 5 minor

Summary. The paper proposes Freqformer, a dual-branch Transformer for image demoiréing that first decomposes the input into high-frequency and low-frequency components via a recursive, dilated low-pass convolution, then processes each branch with a tailored training strategy (crop for high frequency, resize for low frequency), and finally fuses the branches with a learnable Frequency Composition Transform (FCT). The authors report state-of-the-art results on the FHDMi and UHDM benchmarks with a compact 6.065M-parameter model, and support the design with ablations on the frequency decomposition, the FCT, the resize strategy, and the proposed SA-CA module.

Significance. If the results hold, Freqformer is a meaningful contribution to single-image demoiréing: it combines a frequency-decomposition design with an efficient dual-branch transformer and demonstrates competitive or superior performance against both dedicated demoiréing methods and recent general restoration models at a lower parameter count. The paper is strengthened by a public code release, comparisons on two public high-resolution benchmarks, and a coherent set of ablations that isolate the contributions of the main components. However, the central efficiency claim relies on a scale-robustness premise for the low-frequency branch that is asserted with minimal experimental detail, and the reported UHDM margins over the second-best method are small, so the SOTA claim needs stronger evidence and a clarified inference protocol.

major comments (4)

[Sec. 3.2, bullet 2] The claim that the low-frequency component can be downsampled to 0.1x and reconstructed at ~50 dB PSNR is load-bearing for the resize-based training strategy and the low-scale inference, but the supporting experiment is not described: no decomposition level L, dataset, interpolation method, subset size, or variance is reported. Please provide the full protocol and results, including the value of L used, or alternatively reframe this premise as an empirical observation supported by the branch-level results in Table 3 rather than as a general property of the decomposition.
[Sec. 3, first paragraph vs. Sec. 3.2, bullet 4] The test-time protocol is contradictory: Sec. 3 states that during testing both branches operate on the full-resolution image, while Sec. 3.2 bullet 4 states that the low-frequency branch uses the same small-scale input during both training and inference. Please specify the exact inference pipeline, particularly the input resolution of the low branch, how its output is upsampled, and how the upsampled features are aligned with the high-branch features in the FCT before the final reconstruction. This is also needed to interpret the reported 2.49 TFLOPS for 4K inference and the UHDM results.
[Table 1] No error bars, repeated runs, or statistical significance tests are reported. On UHDM, Freqformer's advantage over ESDNet-L is small (SSIM 0.8018 vs. 0.7985; LPIPS 0.2434 vs. 0.2454), so single-run numbers do not establish that the ranking is stable. Please report at least three runs with mean and standard deviation, or a paired comparison, for the UHDM experiments.
[Sec. 3.1, Eq. (2)] The number of decomposition levels L is never specified in the paper, although it controls the cutoff frequency of the low-frequency component and therefore directly affects the validity of the 0.1x resizing claim and the reproducibility of the method. Please state the value of L in Sec. 3.1 and list it in the implementation details.

minor comments (5)

[Sec. 3.2] There are several typos in this section, including 'awesome benifits' and 'reals' (for 'reveals'), which should be corrected.
[Sec. 2.1] The phrase 'Ultr-High-Definition' is missing a hyphen and should read 'Ultra-High-Definition'.
[Sec. 3.1] The expression 'P ostF usion' appears with artificial spacing; this formatting should be fixed to 'PostFusion' throughout.
[Table 4] The row labeled 'Freqformer-L (e2e)' is confusing because no 'Freqformer-L' variant is defined; please clarify whether this is an end-to-end version of Freqformer without frequency decomposition or a different variant.
[Fig. 3] Some notation in Figure 3 (e.g., the projected features with prime symbols and the subscripts) is difficult to read at the printed size; consider enlarging or simplifying the notation in the figure.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: reported results are measured on held-out test data and the frequency-decomposition property, though under-supported, is an empirical claim rather than a definitional reduction.

full rationale

Freqformer's central claims are benchmark comparisons and an architecture; they are not derived from the model's equations in a way that presupposes the outcome. The frequency decomposition (Eq. 2) defines I_l and I_h as recursive convolution/difference, so I_l + I_h = I_m by construction, but the paper never predicts the final demoiréing quality from that identity; it trains on FHDMi/UHDM and reports held-out PSNR/SSIM/LPIPS (Tables 1-2). The resize-based training strategy rests on the empirical scale-robustness assertion in Sec. 3.2 (reconstruction PSNR ~50 dB for I_l), which is under-documented (no decomposition level, dataset, or protocol) and load-bearing for the UHDM margin, but this is a missing-support / reproducibility weakness, not circularity: the claim is an independent measurement, not a fitted parameter renamed as a prediction. The only overlapping-author citations ([39] for channel attention, [48] as a comparison baseline) are not load-bearing for the SOTA claim. The internal inconsistency between Sec. 3 ('In the testing phase, both branches operate on the full-resolution image') and Sec. 3.2 bullet 4 ('same small-scale input during both training and inference') is an ambiguity, not a circular reduction. No step in the paper reduces by construction to its own inputs.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The central claim depends on hand-chosen design constants (kernel k, level L, loss weights, training scales) and on three domain assumptions about how moiré energy separates in frequency. No new physical entities are introduced.

free parameters (4)

Low-pass kernel k = [[1/16,1/8,1/16],[1/8,1/4,1/8],[1/16,1/8,1/16]]
Hand-designed smoothing kernel in Eq. (1). The quality of the frequency separation, and therefore the whole dual-branch design, depends on it, but it is chosen rather than learned or derived.
Decomposition levels L = not reported
The recursive decomposition in Eq. (2) runs for L levels, but L is never given in the implementation details. It controls the low-frequency/high-frequency split and must be guessed for reproduction.
Loss weights lambda1, lambda2 = lambda1 = 1, lambda2 = 0.1
Set 'for simplicity' in Sec. 4. The balance between L1 and perceptual loss affects the final PSNR/SSIM/LPIPS trade-off and is a hand-chosen constant.
Training scales = FHDMi: crop 512, resize 512; UHDM: crop 768, resize 512
The crop and resize sizes determine what the two branches see during training. They are selected by the authors and are load-bearing for the crop/resize strategy claim.

assumptions (3)

domain assumption Moiré patterns separate into high-frequency textures and low-frequency color distortions.
The entire dual-branch design rests on this decomposition of moiré artifacts. The paper supports it with Fig. 2 visualizations and qualitative descriptions, not with a quantitative analysis of energy separation.
domain assumption The low-frequency component is scale-robust and can be downsampled to ~0.1x and resized back with ~50 dB reconstruction PSNR.
This is load-bearing for the resize-based low-frequency branch. It is stated in Sec. 3.2 bullet 2 with a one-sentence, protocol-free experiment, so the reader cannot verify the magnitude of the loss.
domain assumption The high-frequency component has strong spatial locality, so random cropping is sufficient for training.
Stated in Sec. 3.2 bullet 1. No experiment isolates locality; the crop-based training is justified mainly by the final performance of the whole system.

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Cite this review

Pith. "Pith review of Freqformer: Image-Demoir\'eing Transformer via Efficient Frequency Decomposition." pith.science (2026). https://pith.science/paper/6OTWOZFA

@misc{pith2026250519120,
  author       = {Pith},
  title        = {Pith review of: Freqformer: Image-Demoir\'eing Transformer via Efficient Frequency Decomposition},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6OTWOZFA}},
  note         = {Machine review of arXiv:2505.19120}
}

read the original abstract

Image demoir\'eing remains a challenging task due to the complex interplay between texture corruption and color distortions caused by moir\'e patterns. Existing methods, especially those relying on direct image-to-image restoration, often fail to disentangle these intertwined artifacts effectively. While wavelet-based frequency-aware approaches offer a promising direction, their potential remains underexplored. In this paper, we present Freqformer, a Transformer-based framework specifically designed for image demoir\'eing through targeted frequency separation. Our method performs an effective frequency decomposition that explicitly splits moir\'e patterns into high-frequency spatially-localized textures and low-frequency scale-robust color distortions, which are then handled by a dual-branch architecture tailored to their distinct characteristics. We further propose a learnable Frequency Composition Transform (FCT) module to adaptively fuse the frequency-specific outputs, enabling consistent and high-fidelity reconstruction. To better aggregate the spatial dependencies and the inter-channel complementary information, we introduce a Spatial-Aware Channel Attention (SA-CA) module that refines moir\'e-sensitive regions without incurring high computational cost. Extensive experiments on various demoir\'eing benchmarks demonstrate that Freqformer achieves state-of-the-art performance with a compact model size. The code is publicly available at https://github.com/xyLiu339/Freqformer.

Figures

Figures reproduced from arXiv: 2505.19120 by the authors.

**Figure 1.** Frequency Decomposition. To overcome these limitations, we introduce a novel frequency decomposition to efficiently separate moiré textures and color distortions into high-frequency and low-frequency components, respectively ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Visualization of the frequency-decomposed images (zoom in for better analysis). The left [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** The whole pipeline of our Freqformer. The figure shows the dual-branch learning with [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Left part is the detailed transformer architecture of the SA-CA module utilized in all the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Visual comparisons of different baselines on FHDMi and UHDM datasets (please zoom in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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