ErA: Error-Aware Deep Unrolling Network for Single Image Defocus Deblurring

Chan Y. Park; Tu Vo

arxiv: 2606.06540 · v1 · pith:LSZJBHBZnew · submitted 2026-06-04 · 📡 eess.IV · cs.CV

ErA: Error-Aware Deep Unrolling Network for Single Image Defocus Deblurring

Tu Vo , Chan Y. Park This is my paper

Pith reviewed 2026-06-27 23:37 UTC · model grok-4.3

classification 📡 eess.IV cs.CV

keywords defocus deblurringdeep unrollingkernel estimationimage restorationAugmented Lagrangianerror correction

0 comments

The pith

ErA corrects kernel estimation errors in defocus deblurring via an error-aware term in Augmented Lagrangian unrolling.

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

The paper introduces ErA as an end-to-end network for removing defocus blur from single images. It learns a compact kernel basis together with per-pixel weights to represent the blur. An error-aware term is introduced inside the Augmented Lagrangian unrolling, which performs alternating updates together with ResUNet denoisers to reduce mistakes in the estimated kernels. The resulting method records the highest PSNR and SSIM scores on the DPDD, RealDOF and RTF benchmarks and transfers to the CUHK set without any ground-truth supervision.

Core claim

ErA jointly learns a compact kernel basis and per-pixel weights, while an error-aware term in Augmented Lagrangian unrolling corrects kernel estimation errors via alternating updates and ResUNet denoisers.

What carries the argument

Error-aware term in Augmented Lagrangian unrolling that drives alternating updates to correct kernel estimation errors.

If this is right

State-of-the-art PSNR and SSIM on the DPDD, RealDOF and RTF datasets.
Strong generalization to the CUHK dataset in the absence of ground-truth labels.
An end-to-end trainable pipeline that couples kernel-basis learning with iterative error correction.

Where Pith is reading between the lines

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

The same error-correction pattern could be tested on motion-blur or camera-shake removal tasks where kernel estimates are similarly noisy.
If the alternating updates reduce the number of required training examples, the method might lower data demands for other unrolling-based restoration networks.
Real-time mobile photography applications would become feasible only after measuring the runtime cost of the ResUNet steps on embedded hardware.

Load-bearing premise

The error-aware term in the Augmented Lagrangian unrolling effectively corrects kernel estimation errors through alternating updates.

What would settle it

A controlled ablation that removes only the error-aware term and measures a large drop in PSNR on the DPDD test set would confirm its role; absence of any drop would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.06540 by Chan Y. Park, Tu Vo.

**Figure 1.** Figure 1: The predicted defocus blur kernel (left) vs widely assumed Gaussian kernel. (right). (MultiPyramid [38], inverse-kernel [30]) and advanced architectures (IRNeXt [4], Selective Frequency [5], Frequency Selection [3], SSMNet [10], NeumannNet [34]) improve restoration but still assume parametric or uniform PSFs. These assumptions limit their generalization to complex, realworld optics. In contrast, ErA lear… view at source ↗

**Figure 2.** Figure 2: ErA architecture. X0 is initialized by convolving Y with H. Each of the K blocks updates U, E, and X in closed form, while Z and P use a ResUNet CNN. ALM yields closed-form updates for U, X , soft-threshold[11] for E, while Z, P are updated via CNN-based operators Dϕ and Df (ResUNet [6]). Multiplier updates follow standard ALM steps. Please refer to the Appendix section below for more details on solving. U… view at source ↗

**Figure 3.** Figure 3: Visual Comparison of various methods on DPDD (top) and RealDOF (bottom) test set. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

We introduce ErA (Error-Aware Deep Unrolling Network), an end-to-end frame work for single-image defocus deblurring. ErA jointly learns a compact kerne basis and per-pixel weights, while an error-aware term in Augmented Lagrangian unrolling corrects kernel estimation errors via alternating updates and ResUNet denoisers. It achieves state-of-the-art PSNR/SSIM on DPDD, RealDOF, and RTF, and shows strong generalization on CUHK without ground truth.

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

ErA adds an error-aware correction inside Augmented Lagrangian unrolling for defocus deblurring and reports SOTA numbers on the standard benchmarks, but the abstract gives almost no experimental detail to judge whether the gains are real.

read the letter

The one thing to know is that this paper takes a standard deep-unrolling setup for single-image defocus deblurring and inserts an extra error-aware term that is supposed to fix mistakes in the estimated kernel during the alternating updates. It also learns a compact kernel basis together with per-pixel weights and plugs in ResUNet denoisers. On paper that produces the usual SOTA PSNR/SSIM numbers on DPDD, RealDOF and RTF plus decent generalization on CUHK.

The new piece is the explicit error-aware correction inside the unrolling loop. Most prior unrolling work for deblurring already alternates between kernel and image updates; the claim here is that adding a term that directly penalizes kernel error improves the estimates enough to matter. That is a modest but concrete change rather than a wholesale redesign.

The method description is clear enough on the high level, and the choice to keep the kernel basis small while allowing per-pixel modulation is sensible for spatially varying defocus. Reporting results without ground truth on CUHK is also a reasonable check.

The soft spot is that the abstract supplies no numbers, no ablation tables, no error bars, and no list of baselines. We cannot tell whether the error-aware term actually drives the improvement or whether the gains come from a stronger backbone, different training schedule, or simply more careful tuning. Without those controls the central claim stays untested. The paper also does not discuss how sensitive the alternating updates are to initialization or how the error term is weighted in practice.

This is a narrow but useful incremental step for people who already work on defocus deblurring pipelines. A reader who needs a drop-in network for consumer photography or who wants to compare unrolling variants would find it worth reading. It is not going to change the broader field.

I would send it to peer review. The idea is straightforward to evaluate once the experiments are on the table, and the authors have at least framed a testable modification rather than a black-box claim.

Referee Report

1 major / 1 minor

Summary. The paper introduces ErA, an end-to-end deep unrolling network for single-image defocus deblurring. It jointly learns a compact kernel basis and per-pixel weights, and incorporates an error-aware term within Augmented Lagrangian unrolling that corrects kernel estimation errors through alternating updates and ResUNet denoisers. The method is reported to achieve state-of-the-art PSNR/SSIM on the DPDD, RealDOF, and RTF datasets while demonstrating strong generalization on the CUHK dataset without ground truth.

Significance. If the performance claims are substantiated, the work offers a potentially useful integration of error-aware correction into optimization unrolling for defocus deblurring, addressing a common source of error in kernel-based methods. The combination of learned kernel basis with alternating updates and learned denoisers could provide a template for similar inverse problems, though the absence of detailed experimental validation in the supplied text limits assessment of its impact.

major comments (1)

[Abstract and results sections] The central performance claim of state-of-the-art results cannot be evaluated because the supplied manuscript text provides no experimental details, error bars, baselines, ablation studies, or quantitative tables supporting the PSNR/SSIM gains on DPDD, RealDOF, RTF, or generalization on CUHK.

minor comments (1)

[Abstract] Abstract contains typographical errors: 'frame work' should be 'framework' and 'kerne basis' should be 'kernel basis'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for reviewing our manuscript on ErA. The main concern is that experimental details supporting the state-of-the-art claims are absent from the supplied text. We address this point directly below.

read point-by-point responses

Referee: [Abstract and results sections] The central performance claim of state-of-the-art results cannot be evaluated because the supplied manuscript text provides no experimental details, error bars, baselines, ablation studies, or quantitative tables supporting the PSNR/SSIM gains on DPDD, RealDOF, RTF, or generalization on CUHK.

Authors: The full manuscript includes a dedicated Experiments section (Section 4) containing quantitative tables with PSNR/SSIM results on DPDD, RealDOF, and RTF, direct comparisons against multiple baselines, ablation studies isolating the contributions of the compact kernel basis, per-pixel weights, and error-aware term, and generalization results on CUHK. Error bars are reported for repeated runs on key metrics. These elements are already present and directly support the performance claims; we refer the referee to that section for the requested details. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The abstract provides only a high-level description of the ErA framework with no equations, derivations, or mathematical steps shown. No load-bearing claims reduce to self-definition, fitted inputs renamed as predictions, or self-citation chains. The method is presented as an empirical end-to-end network achieving performance metrics, with no internal derivation chain available for inspection that could exhibit circularity by construction. This is the expected outcome when no specific equations are supplied.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no information on free parameters, axioms, or invented entities; all fields left empty.

pith-pipeline@v0.9.1-grok · 5605 in / 1134 out tokens · 20919 ms · 2026-06-27T23:37:17.488335+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

39 extracted references · 3 canonical work pages · 1 internal anchor

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J. Park, Y .-W. Tai, D. Cho, and I. So Kweon. A unified approach of multi-scale deep and hand- crafted features for defocus estimation. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1736–1745, 2017

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Y . Quan, Z. Wu, and H. Ji. Gaussian kernel mixture network for single image defocus deblurring. Advances in Neural Information Processing Systems, 34:20812–20824, 2021

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L. Ruan, B. Chen, J. Li, and M. Lam. Learning to deblur using light field generated and real defocus images. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16304–16313, 2022

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C. J. Schuler, M. Hirsch, S. Harmeling, and B. Schölkopf. Learning to deblur.IEEE transactions on pattern analysis and machine intelligence, 38(7):1439–1451, 2015

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J. Shi, L. Xu, and J. Jia. Just noticeable defocus blur detection and estimation. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 657–665, 2015

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H. Son, J. Lee, S. Cho, and S. Lee. Single image defocus deblurring using kernel-sharing parallel atrous convolutions. InProceedings of the IEEE International Conference on Computer Vision, pages 2642–2650, 2021

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P. Tang, Z. Xu, C. Zhou, P. Wei, P. Han, X. Cao, and T. Lasser. Prior and prediction inverse kernel transformer for single image defocus deblurring.Proceedings of the AAAI Conference on Artificial Intelligence, 38(6):5145–5153, Mar. 2024. doi: 10.1609/aaai.v38i6.28320. URL https://ojs.aaai.org/index.php/AAAI/article/view/28320

work page doi:10.1609/aaai.v38i6.28320 2024
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X. Tao, H. Gao, X. Shen, J. Wang, and J. Jia. Scale-recurrent network for deep image deblurring. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 8174–8182, 2018

2018
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V o and C

T. V o and C. Y . Park. Deep joint unrolling for deblurring and low-light image enhancement (jude). In2025 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), pages 2696–2705. IEEE, 2025

2025
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G. Xu, Y . Quan, and H. Ji. Estimating defocus blur via rank of local patches. InProceedings of the IEEE international conference on computer vision, pages 5371–5379, 2017

2017
[34]

Z. W. Yuhui Quan and H. Ji. Neumann network with recursive kernels for single image defocus deblurring. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5754–5763, 2023

2023
[35]

Zhang, J

J. Zhang, J. Pan, W.-S. Lai, R. W. Lau, and M.-H. Yang. Learning fully convolutional networks for iterative non-blind deconvolution. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3817–3825, 2017. 6

2017
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Zhang, J

J. Zhang, J. Pan, J. Ren, Y . Song, L. Bao, R. W. Lau, and M.-H. Yang. Dynamic scene deblurring using spatially variant recurrent neural networks. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 2521–2529, 2018

2018
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Zhang, L

K. Zhang, L. V . Gool, and R. Timofte. Deep unfolding network for image super-resolution. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3217–3226, 2020

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Zhang, P

Y . Zhang, P. Zheng, W. Yan, C. Fang, and S. S. Cheng. A unified framework for microscopy defocus deblur with multi-pyramid transformer and contrastive learning. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11125–11136, 2024

2024
[39]

W. Zuo, D. Ren, D. Zhang, S. Gu, and L. Zhang. Learning iteration-wise generalized shrinkage– thresholding operators for blind deconvolution.IEEE Transactions on Image Processing, 25(4): 1751–1764, 2016. 7 6 Appendix 6.1 Derivation of closed-form solution In this section, we will provide the complete closed-form solutions for each variable described in Se...

2016

[1] [1]

Abuolaim and M

A. Abuolaim and M. S. Brown. Defocus deblurring using dual-pixel data. InComputer Vision– ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part X 16, pages 111–126. Springer, 2020

2020

[2] [2]

Carbajal, P

G. Carbajal, P. Vitoria, M. Delbracio, P. Musé, and J. Lezama. Non-uniform blur kernel estimation via adaptive basis decomposition.arXiv preprint arXiv:2102.01026, 2021

work page arXiv 2021

[3] [3]

Y . Cui, W. Ren, X. Cao, and A. Knoll. Image restoration via frequency selection.IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(2):1093–1108, 2023

2023

[4] [4]

Y . Cui, W. Ren, S. Yang, X. Cao, and A. Knoll. Irnext: Rethinking convolutional network design for image restoration. InProceedings of the 40th International Conference on Machine Learning, 2023

2023

[5] [5]

Y . Cui, Y . Tao, Z. Bing, W. Ren, X. Gao, X. Cao, K. Huang, and A. Knoll. Selective fre- quency network for image restoration. InThe eleventh international conference on learning representations, 2023

2023

[6] [6]

F. I. Diakogiannis, F. Waldner, P. Caccetta, and C. Wu. Resunet-a: A deep learning framework for semantic segmentation of remotely sensed data.ISPRS Journal of Photogrammetry and Remote Sensing, 162:94–114, 2020

2020

[7] [7]

W. Dong, P. Wang, W. Yin, G. Shi, F. Wu, and X. Lu. Denoising prior driven deep neural network for image restoration.IEEE transactions on pattern analysis and machine intelligence, 41(10):2305–2318, 2018

2018

[8] [8]

D’Andrès, J

L. D’Andrès, J. Salvador, A. Kochale, and S. Süsstrunk. Non-parametric blur map regression for depth of field extension.IEEE Transactions on Image Processing, 25(4):1660–1673, 2016

2016

[9] [9]

H. Gao, X. Tao, X. Shen, and J. Jia. Dynamic scene deblurring with parameter selective sharing and nested skip connections. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3848–3856, 2019

2019

[10] [10]

H. Gao, B. Ma, Y . Zhang, J. Yang, J. Yang, and D. Dang. Learning enriched features via selective state spaces model for efficient image deblurring. InProceedings of the 32nd ACM International Conference on Multimedia, pages 710–718, 2024

2024

[11] [11]

E. T. Hale, W. Yin, and Y . Zhang. Fixed-point continuation for\ell_1-minimization: Methodol- ogy and convergence.SIAM Journal on Optimization, 19(3):1107–1130, 2008

2008

[12] [12]

Ji and K

H. Ji and K. Wang. Robust image deblurring with an inaccurate blur kernel.IEEE Transactions on Image processing, 21(4):1624–1634, 2011

2011

[13] [13]

Karaali and C

A. Karaali and C. R. Jung. Edge-based defocus blur estimation with adaptive scale selection. IEEE Transactions on Image Processing, 27(3):1126–1137, 2017

2017

[14] [14]

Karaali and C

A. Karaali and C. R. Jung. Svbr-net: A non-blind spatially varying defocus blur removal network. In2022 IEEE International Conference on Image Processing (ICIP), pages 566–570. IEEE, 2022

2022

[15] [15]

D. P. Kingma and J. Ba. Adam: A method for stochastic optimization.arXiv preprint arXiv:1412.6980, 2014

work page internal anchor Pith review Pith/arXiv arXiv 2014

[16] [16]

Krishnan and R

D. Krishnan and R. Fergus. Fast image deconvolution using hyper-laplacian priors.Advances in neural information processing systems, 22, 2009

2009

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J. Lee, S. Lee, S. Cho, and S. Lee. Deep defocus map estimation using domain adaptation. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 12222–12230, 2019

2019

[18] [18]

J. Lee, H. Son, J. Rim, S. Cho, and S. Lee. Iterative filter adaptive network for single image defocus deblurring. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2034–2042, 2021. 5

2034

[19] [19]

Y . Li, M. Tofighi, V . Monga, and Y . C. Eldar. An algorithm unrolling approach to deep image deblurring. InICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 7675–7679. IEEE, 2019

2019

[20] [20]

S. Nah, T. Hyun Kim, and K. Mu Lee. Deep multi-scale convolutional neural network for dynamic scene deblurring. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 3883–3891, 2017

2017

[21] [21]

Nan and H

Y . Nan and H. Ji. Deep learning for handling kernel/model uncertainty in image deconvolution. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 2388–2397, 2020

2020

[22] [22]

Y . Nan, Y . Quan, and H. Ji. Variational-em-based deep learning for noise-blind image deblurring. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3626–3635, 2020

2020

[23] [23]

Park, Y .-W

J. Park, Y .-W. Tai, D. Cho, and I. So Kweon. A unified approach of multi-scale deep and hand- crafted features for defocus estimation. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 1736–1745, 2017

2017

[24] [24]

Punnappurath, A

A. Punnappurath, A. Abuolaim, M. Afifi, and M. S. Brown. Modeling defocus-disparity in dual-pixel sensors. In2020 IEEE International Conference on Computational Photography (ICCP), pages 1–12. IEEE, 2020

2020

[25] [25]

Y . Quan, Z. Wu, and H. Ji. Gaussian kernel mixture network for single image defocus deblurring. Advances in Neural Information Processing Systems, 34:20812–20824, 2021

2021

[26] [26]

L. Ruan, B. Chen, J. Li, and M. Lam. Learning to deblur using light field generated and real defocus images. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16304–16313, 2022

2022

[27] [27]

C. J. Schuler, M. Hirsch, S. Harmeling, and B. Schölkopf. Learning to deblur.IEEE transactions on pattern analysis and machine intelligence, 38(7):1439–1451, 2015

2015

[28] [28]

J. Shi, L. Xu, and J. Jia. Just noticeable defocus blur detection and estimation. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 657–665, 2015

2015

[29] [29]

H. Son, J. Lee, S. Cho, and S. Lee. Single image defocus deblurring using kernel-sharing parallel atrous convolutions. InProceedings of the IEEE International Conference on Computer Vision, pages 2642–2650, 2021

2021

[30] [30]

P. Tang, Z. Xu, C. Zhou, P. Wei, P. Han, X. Cao, and T. Lasser. Prior and prediction inverse kernel transformer for single image defocus deblurring.Proceedings of the AAAI Conference on Artificial Intelligence, 38(6):5145–5153, Mar. 2024. doi: 10.1609/aaai.v38i6.28320. URL https://ojs.aaai.org/index.php/AAAI/article/view/28320

work page doi:10.1609/aaai.v38i6.28320 2024

[31] [31]

X. Tao, H. Gao, X. Shen, J. Wang, and J. Jia. Scale-recurrent network for deep image deblurring. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 8174–8182, 2018

2018

[32] [32]

V o and C

T. V o and C. Y . Park. Deep joint unrolling for deblurring and low-light image enhancement (jude). In2025 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), pages 2696–2705. IEEE, 2025

2025

[33] [33]

G. Xu, Y . Quan, and H. Ji. Estimating defocus blur via rank of local patches. InProceedings of the IEEE international conference on computer vision, pages 5371–5379, 2017

2017

[34] [34]

Z. W. Yuhui Quan and H. Ji. Neumann network with recursive kernels for single image defocus deblurring. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5754–5763, 2023

2023

[35] [35]

Zhang, J

J. Zhang, J. Pan, W.-S. Lai, R. W. Lau, and M.-H. Yang. Learning fully convolutional networks for iterative non-blind deconvolution. InProceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 3817–3825, 2017. 6

2017

[36] [36]

Zhang, J

J. Zhang, J. Pan, J. Ren, Y . Song, L. Bao, R. W. Lau, and M.-H. Yang. Dynamic scene deblurring using spatially variant recurrent neural networks. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 2521–2529, 2018

2018

[37] [37]

Zhang, L

K. Zhang, L. V . Gool, and R. Timofte. Deep unfolding network for image super-resolution. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 3217–3226, 2020

2020

[38] [38]

Zhang, P

Y . Zhang, P. Zheng, W. Yan, C. Fang, and S. S. Cheng. A unified framework for microscopy defocus deblur with multi-pyramid transformer and contrastive learning. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11125–11136, 2024

2024

[39] [39]

W. Zuo, D. Ren, D. Zhang, S. Gu, and L. Zhang. Learning iteration-wise generalized shrinkage– thresholding operators for blind deconvolution.IEEE Transactions on Image Processing, 25(4): 1751–1764, 2016. 7 6 Appendix 6.1 Derivation of closed-form solution In this section, we will provide the complete closed-form solutions for each variable described in Se...

2016