arxiv: 2605.10583 · v1 · submitted 2026-05-11 · 💻 cs.CV

Recognition: 2 theorem links

· Lean Theorem

FrequencyCT: Frequency domain pseudo-label generation for self-supervised low-dose CT denoising

Guoquan Wei , Liu Shi , Chong Chen , Qiegen Liu

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:39 UTC · model grok-4.3

classification 💻 cs.CV

keywords low-dose CT denoisingself-supervised learningfrequency domainpseudo-label generationzero-shot denoisingprojection data

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The pith

Frequency-domain anchoring and perturbation generate pseudo-labels that train a denoiser on noisy low-dose CT data alone.

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

The paper sets out to show that low-dose CT denoising can be performed in a fully self-supervised way by shifting the label-generation step into the frequency domain. Because noise and underlying signal separate more cleanly across frequencies than in the spatial domain, the authors anchor the low-frequency content and then apply controlled amplitude and mask changes in the high-frequency region to synthesize training pairs. These pairs are further truncated to counteract the varying noise variance seen in real projections. If the separation holds, a network trained this way can be applied directly to new noisy scans without ever seeing a clean reference image. The result would remove the need for paired high-dose and low-dose acquisitions that are currently required for supervised training.

Core claim

FrequencyCT creates usable pseudo-label data for self-supervision by first anchoring low-frequency coefficients, then performing phase-preserving amplitude modulation together with high-frequency mask perturbation, and finally truncating the resulting samples to stabilize gradient flow during training of a denoising network on low-dose CT projections.

What carries the argument

Regional low-frequency anchoring combined with phase-preserving amplitude modulation and high-frequency mask perturbation, which together isolate noise characteristics in the frequency domain to synthesize pseudo-labels.

If this is right

The method runs in a zero-shot self-supervised regime, needing no paired clean data for either training or deployment.
Truncation of generated samples counters the effect of fluctuating projection noise variance and keeps optimization stable.
Performance is reported on both public benchmark datasets and real-world clinical acquisitions, indicating direct applicability.

Where Pith is reading between the lines

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

The same frequency-separation idea for creating pseudo-labels could be tried on other modalities whose noise exhibits different spectral behavior, such as PET or ultrasound.
If the pseudo-labels prove sufficiently faithful, the approach would support routine use of lower radiation-dose CT protocols without requiring new supervised datasets.
The truncation step suggests that any frequency-based pseudo-label method may need an explicit variance-stabilization stage when applied to real acquisition data.

Load-bearing premise

The frequency domain largely isolates noise from the clean signal, so that low-frequency anchoring plus high-frequency perturbation produces reliable training targets.

What would settle it

A controlled experiment in which networks trained on the generated pseudo-labels show no denoising gain, or even degrade image quality, when compared with the same architecture trained on the raw noisy inputs alone.

Figures

Figures reproduced from arXiv: 2605.10583 by Chong Chen, Guoquan Wei, Liu Shi, Qiegen Liu.

**Figure 1.** Figure 1: Description of different self-supervised methods in the projection domain. operations, such as masking [19] or non-local search [20], within the image domain. However, these strategies frequently cause structural leakage when confronting long-range correlated noise in LDCT. Although the projection domain offers a more physically grounded foundation, relying solely on spatial manipulations within it still … view at source ↗

**Figure 2.** Figure 2: This figure illustrates the noise distribution characteristics in the frequency domain and provides a brief overview of inspired pseudolabel generation. low-frequency region Alow, interferes with the amplitude of Ahigh. That is, while minimizing damage to the underlying anatomical semantics, it physically severs or reshapes the correlation of noise. B. Proposed FrequencyCT Based on the above motivation, i… view at source ↗

**Figure 4.** Figure 4: Detailed description of data truncation training and inference. Algorithm 1 Training and Inference Process Input: Single LDCT projection data pld, dynamic modulation range Rrand, number of samples n Output: Denoised data p and image x0 Training Phase: 1: Generate noise and mask bank using Eqs. (4) and (5) 2: Repeat 3: Update fθ by Eq. (8) 4: Until converged Inference Phase: 5: p ← fθ ∗ (pld) 6: x0 = FBP(p)… view at source ↗

**Figure 3.** Figure 3: Description of generating pseudo-samples using noise perturbation and mask perturbation. In summary, pseudo-label generation can be described as follows: after obtaining the LDCT projection pld, perform a Fourier transform on it to the frequency domain, and apply PPAM and PPSM at the same time to generate a noise bank and a mask bank, as detailed in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 5.** Figure 5: (a) Experimental validation of Eq. (9) using LDCT projection and clean data. (b) Validation of the fit after taking ln(·) on both sides of Eq. (9) and display of the correlation coefficient. (c) PCA of pseudo-samples generated by different perturbation operators before truncation, along with source noise and reference data. (d) PCA of pseudo-samples generated by different perturbation operators after trunc… view at source ↗

**Figure 6.** Figure 6: Comparison of real-world human and mouse data with different methods. SNR and CNR were calculated for each experimental result, and the yellow dashed line represents the background region used in the calculation, and the blue line represents the region of interest. Additionally, the lower left corner of each image displays NPS to demonstrate the superiority of FrequencyCT. 2) Implementation Details: This s… view at source ↗

**Figure 7.** Figure 7: Quantitative results of denoising from different doses and simulation data. The blue boxes in the figure represent the regions of interest for each image, and the lower-left corner shows the performance of the denoised images in the frequency domain [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

read the original abstract

Despite extensive research on computed tomography (CT) denoising, few studies exploit projection-domain data characteristics to mitigate noise correlation. To address this, this work proposes FrequencyCT, the first zero-shot self-supervised method for pseudo-label generation in the frequency domain for low-dose CT denoising. Leveraging the characteristic of the frequency domain that largely isolates noise from clean signals, a regional low-frequency anchoring technique is proposed. Phase-preserving amplitude modulation and mask perturbation in the high-frequency region generate pseudo-label data for self-supervision. The fluctuating noise variance in the projection domain prompts truncation of the generated samples to stabilize the network's optimization gradient. Evaluation results on multiple public and real-world datasets confirm the clinical application potential of this research, which will have a revolutionary impact on the field of denoising. The code can be obtained from https://github.com/yqx7150/FrequencyCT.

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

FrequencyCT's frequency-domain pseudo-label pipeline is a coherent new angle on self-supervised low-dose CT denoising, but the real test is whether the reported gains over baselines are consistent and practically meaningful.

read the letter

The paper's main contribution is a zero-shot self-supervised scheme that generates pseudo-labels by anchoring low-frequency content regionally, then applying phase-preserving amplitude modulation and high-frequency mask perturbation in the projection domain. This targets the noise correlation problem that paired-data methods often ignore, and the truncation step for gradient stability is a sensible practical touch. They also release code, which helps anyone wanting to check the implementation directly. That combination of domain-specific signal separation and explicit stabilization steps is what stands out as new relative to prior self-supervised CT work that mostly stays in image space or relies on simpler noise models. The evaluations on public and real-world datasets are the part that matters most for whether this moves the needle on radiation reduction. If those show clear, reproducible improvements with ablations that isolate the frequency components, the method earns its place. The soft spot is the abstract's language about revolutionary clinical impact; that overstates what any single denoising paper can deliver without large-scale reader studies or dose-reduction trials. The central frequency-isolation premise is standard signal-processing practice rather than a breakthrough assumption, so the paper stands or falls on the quantitative results and how well they generalize beyond the tested scanners. This is worth a serious referee for groups working on medical image restoration or unpaired learning, especially if they already care about projection-domain data. A reader who needs a new baseline or wants to adapt frequency tricks to other modalities would get concrete value once the numbers are scrutinized. I would send it to peer review rather than desk-reject, with the expectation that revisions tighten the claims and add missing controls.

Referee Report

1 major / 1 minor

Summary. The manuscript proposes FrequencyCT, the first zero-shot self-supervised method for pseudo-label generation in the frequency domain for low-dose CT denoising. It leverages frequency-domain isolation of noise via a regional low-frequency anchoring technique, combined with phase-preserving amplitude modulation and high-frequency mask perturbation to generate pseudo-labels, and applies sample truncation to stabilize optimization gradients amid fluctuating noise variance in the projection domain. Evaluations on multiple public and real-world datasets are presented to support claims of clinical application potential.

Significance. If the quantitative results hold, the work offers a coherent pipeline for self-supervised CT denoising that directly targets projection-domain noise correlation through frequency-domain operations, which is a useful extension of standard signal-processing heuristics. The explicit stabilization steps (truncation) and open-sourced code are strengths that aid reproducibility. The approach could reduce reliance on paired clean/noisy data, a persistent bottleneck in medical imaging, though its practical significance depends on demonstrated gains over existing self-supervised baselines.

major comments (1)

Abstract: the assertion that the research 'will have a revolutionary impact on the field of denoising' is disproportionate to the described evidence and should be replaced with a measured statement of specific contributions relative to prior self-supervised CT denoising methods.

minor comments (1)

Abstract: the description of the method components is clear, but the absence of any numerical results, baseline names, or dataset identifiers makes it difficult for readers to gauge the scale of improvement; the results section should include these details with error bars.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We agree that the language in the abstract overstates the potential impact and have revised it to a measured statement focused on our specific contributions relative to prior self-supervised CT denoising methods.

read point-by-point responses

Referee: Abstract: the assertion that the research 'will have a revolutionary impact on the field of denoising' is disproportionate to the described evidence and should be replaced with a measured statement of specific contributions relative to prior self-supervised CT denoising methods.

Authors: We acknowledge that the original phrasing was disproportionate to the presented evidence. In the revised manuscript, the final sentence of the abstract has been changed to: 'Evaluation results on multiple public and real-world datasets confirm the clinical application potential of this research, which introduces a zero-shot self-supervised approach for low-dose CT denoising via frequency-domain pseudo-label generation.' This provides a specific, evidence-based description of the contributions without hyperbolic claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's core pipeline generates pseudo-labels via explicit frequency-domain operations (regional low-frequency anchoring, phase-preserving amplitude modulation, high-frequency mask perturbation, and sample truncation) applied directly to the input noisy projections. These steps are deterministic transformations of the observed data and do not reduce any claimed output or prediction to a fitted parameter or self-referential definition. No self-citations appear as load-bearing premises, no uniqueness theorems are invoked, and the self-supervised training objective remains independent of the final denoised result. The derivation is therefore self-contained against external benchmarks and standard frequency-domain heuristics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that noise and signal are largely separable in the frequency domain; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)

domain assumption The frequency domain largely isolates noise from clean signals
This separation is invoked to justify the regional low-frequency anchoring and high-frequency perturbation steps.

pith-pipeline@v0.9.0 · 5447 in / 1243 out tokens · 69672 ms · 2026-05-12T03:39:33.752574+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Leveraging the characteristic of the frequency domain that largely isolates noise from clean signals, a regional low-frequency anchoring technique is proposed. Phase-preserving amplitude modulation and mask perturbation in the high-frequency region generate pseudo-label data
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean embed_strictMono_of_one_lt unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 1... σ²_y ≈ exp(p)/I0 ... truncation of the generated samples to stabilize the network's optimization gradient

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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