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arxiv: 2604.15681 · v1 · submitted 2026-04-17 · 💻 cs.CV

Self-Supervised Angular Deblurring in Photoacoustic Reconstruction via Noisier2Inverse

Markus Haltmeier , Nadja Gruber , Gyeongha Hwang This is my paper

Pith reviewed 2026-05-10 09:07 UTC · model grok-4.3

classification 💻 cs.CV
keywords photoacoustic tomographyself-supervised learningimage reconstructionangular deblurringfinite-size detectorsNoisier2Inverse
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The pith

A self-supervised Noisier2Inverse method in polar coordinates recovers sharp photoacoustic images from finite-size detectors using only noisy measurements.

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

The paper establishes a ground-truth-free reconstruction technique for photoacoustic tomography that corrects the systematic blurring caused by real finite-size detectors. It recasts the problem as angular deblurring and applies a Noisier2Inverse framework directly in the polar domain, where the detector's angular point-spread function is known and can be used to generate noisier training pairs from the available data. A statistically grounded early-stopping rule further stabilizes the training. If correct, this removes the need for paired clean images that are hard to obtain in practice, while still delivering image quality close to fully supervised approaches.

Core claim

The authors show that finite-detector photoacoustic reconstruction reduces to an angular deblurring task in polar coordinates. By embedding the known angular point-spread function into a Noisier2Inverse self-supervised loop and adding an early-stopping criterion derived from the noise statistics, the method learns to invert the blur operator from noisy measurements alone, without any ground-truth pressure distributions.

What carries the argument

Polar-domain Noisier2Inverse formulation that uses the known angular point-spread function to create self-supervised training pairs for angular deblurring.

If this is right

  • The approach works on real measured data with finite-size detectors and requires no simulated ground-truth pairs.
  • Image quality approaches that of supervised learning methods while remaining fully self-supervised.
  • A novel early-stopping rule based on noise statistics prevents over-fitting during training.
  • The method consistently beats other unsupervised baselines in the reported experiments.

Where Pith is reading between the lines

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

  • The same angular-deblurring reformulation could be tested in other tomographic modalities that share a known detector response.
  • Performance on detectors with varying sizes or non-circular geometries would provide a direct test of how sensitive the method is to the accuracy of the point-spread function.
  • If the early-stopping rule generalizes, it might reduce the need for manual validation sets in other self-supervised inverse-problem settings.

Load-bearing premise

The angular point-spread function of the finite-size detectors must be known accurately enough to be used directly in the polar-domain Noisier2Inverse training without ground-truth images.

What would settle it

If reconstructions obtained by feeding the method an intentionally inaccurate angular point-spread function become visibly worse than standard filtered back-projection on the same data, the core modeling assumption would be falsified.

Figures

Figures reproduced from arXiv: 2604.15681 by Gyeongha Hwang, Markus Haltmeier, Nadja Gruber.

Figure 3.1
Figure 3.1. Figure 3.1: Comparison between EMDk on the validation set (black) and PSNR at iteration k on the test set (orange) for four different blurring kernels. All results consistently show an inverse relationship between these quantities. 4 Numerical simulations In this section we present numerical experiments of the self-supervised discrete reconstruction framework outlined in Algorithm 1. All experiments were conducted i… view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Example reconstruction across blur types (subfigures). Within each subfigure, the [PITH_FULL_IMAGE:figures/full_fig_p015_4_1.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Same setup as Fig. 4.1, with a different ground-truth sample. [PITH_FULL_IMAGE:figures/full_fig_p016_4_2.png] view at source ↗
read the original abstract

Photoacoustic tomography (PAT) is an emerging imaging modality that combines the complementary strengths of optical contrast and ultrasonic resolution. A central task is image reconstruction, where measured acoustic signals are used to recover the initial pressure distribution. For ideal point-like or line-like detectors, several efficient and fast reconstruction algorithms exist, including Fourier methods, filtered backprojection, and time reversal. However, when applied to data acquired with finite-size detectors, these methods yield systematically blurred images. Although sharper images can be obtained by compensating for finite-detector effects, supervised learning approaches typically require ground-truth images that may not be available in practice. We propose a self-supervised reconstruction method based on Noisier2Inverse that addresses finite-size detector effects without requiring ground-truth data. Our approach operates directly on noisy measurements and learns to recover high-quality PAT images in a ground-truth-free manner. Its key components are: (i) PAT-specific modeling that recasts the problem as angular deblurring; (ii) a Noisier2Inverse formulation in the polar domain that leverages the known angular point-spread function; and (iii) a novel, statistically grounded early-stopping rule. In experiments, the proposed method consistently outperforms alternative approaches that do not use supervised data and achieves performance close to supervised benchmarks, while remaining practical for real acquisitions with finite-size detectors.

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.

Referee Report

2 major / 2 minor

Summary. The paper proposes a self-supervised reconstruction method for photoacoustic tomography (PAT) images acquired with finite-size detectors. It recasts finite-detector blurring as angular deblurring, formulates a Noisier2Inverse objective in the polar domain that directly incorporates the known angular point-spread function (PSF), and introduces a statistically grounded early-stopping rule. Experiments are claimed to show consistent outperformance over unsupervised baselines and performance close to supervised methods, while remaining practical for real acquisitions.

Significance. If the central claims hold, the work would provide a practical route to high-quality PAT reconstruction without ground-truth images, which is a significant advantage over supervised learning approaches that often require unavailable paired data. The polar-domain Noisier2Inverse formulation and early-stopping rule represent targeted adaptations that could generalize to other limited-view or finite-aperture imaging problems.

major comments (2)
  1. [Abstract, §3] Abstract and §3 (method description): The central claim of ground-truth-free training and consistent outperformance rests on the assumption that the angular PSF of finite-size detectors is known with sufficient fidelity to be plugged directly into the Noisier2Inverse objective. The manuscript provides no sensitivity analysis or robustness tests against unmodeled effects such as bandwidth limits, positioning jitter, or acoustic attenuation, which could cause residual blur or artifacts and undermine the reported gains over unsupervised baselines.
  2. [Experimental results] Experimental results section: The abstract states that the method 'consistently outperforms alternative approaches that do not use supervised data and achieves performance close to supervised benchmarks,' yet the provided text contains no details on dataset composition, number of samples, error bars, statistical significance tests, or cross-validation procedure. Without these, the load-bearing performance claims cannot be verified and the proximity to supervised results remains unquantified.
minor comments (2)
  1. [§3] Notation for the polar-domain transformation and the exact form of the Noisier2Inverse loss should be defined explicitly with equations rather than described at a high level.
  2. [Abstract, §3] The statistically grounded early-stopping rule is mentioned as novel but its derivation or statistical justification is not detailed in the abstract; a brief derivation or reference to the underlying statistical principle would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight important aspects for strengthening the manuscript. We address each major point below and will revise the paper accordingly to improve transparency and robustness.

read point-by-point responses

  1. Referee: [Abstract, §3] Abstract and §3 (method description): The central claim of ground-truth-free training and consistent outperformance rests on the assumption that the angular PSF of finite-size detectors is known with sufficient fidelity to be plugged directly into the Noisier2Inverse objective. The manuscript provides no sensitivity analysis or robustness tests against unmodeled effects such as bandwidth limits, positioning jitter, or acoustic attenuation, which could cause residual blur or artifacts and undermine the reported gains over unsupervised baselines.

    Authors: We agree that the absence of sensitivity analysis is a limitation. Our formulation assumes the angular PSF (derived from detector geometry) is known to sufficient accuracy for the Noisier2Inverse objective in polar coordinates, which is a standard modeling choice for finite-aperture effects. However, real-world discrepancies from bandwidth limits, jitter, or attenuation could indeed reduce the reported gains. In the revised manuscript, we will add a dedicated robustness subsection with experiments that systematically perturb the PSF (e.g., width variations of ±5–15%, added Gaussian jitter, and frequency-dependent attenuation) and quantify the resulting changes in PSNR/SSIM relative to unsupervised baselines and supervised references. revision: yes

  2. Referee: [Experimental results] Experimental results section: The abstract states that the method 'consistently outperforms alternative approaches that do not use supervised data and achieves performance close to supervised benchmarks,' yet the provided text contains no details on dataset composition, number of samples, error bars, statistical significance tests, or cross-validation procedure. Without these, the load-bearing performance claims cannot be verified and the proximity to supervised results remains unquantified.

    Authors: The referee is correct; the current manuscript text does not include explicit details on dataset sizes, error bars, statistical tests, or cross-validation, which weakens verifiability of the performance claims. We will revise the experimental results section by adding: (i) a summary table of dataset composition (e.g., number of simulated phantoms, real acquisitions, and train/validation/test splits); (ii) mean ± standard deviation metrics from multiple independent runs; (iii) p-values from paired statistical tests against baselines; and (iv) a description of the cross-validation procedure. These additions will quantify the outperformance and proximity to supervised results. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the derivation chain

full rationale

The paper's central derivation recasts finite-size detector effects as angular deblurring in the polar domain and applies a Noisier2Inverse formulation that leverages the known angular PSF together with a statistically grounded early-stopping rule. This chain relies on established domain knowledge of the PSF and on the external Noisier2Inverse framework rather than any self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation that reduces the result to its own inputs by construction. Experimental claims of outperformance are benchmarked against independent unsupervised and supervised baselines and do not collapse to tautological fits. The method therefore remains self-contained against external benchmarks, consistent with the default expectation that most papers exhibit no circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard mathematical properties of inverse problems and the Noisier2Inverse framework, plus the domain assumption that the angular PSF is known and usable in polar coordinates. No free parameters or new entities are introduced in the abstract description.

axioms (2)
  • domain assumption The angular point-spread function for finite-size detectors is known and can be directly incorporated into the polar-domain reconstruction model.
    Explicitly listed as key component (ii) of the approach.
  • domain assumption Noisier2Inverse can be adapted to the PAT angular deblurring task while preserving its self-supervised properties.
    Core of the proposed formulation.

pith-pipeline@v0.9.0 · 5538 in / 1331 out tokens · 35566 ms · 2026-05-10T09:07:27.163436+00:00 · methodology

discussion (0)

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