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arxiv: 2607.00251 · v1 · pith:PXVSFNO3new · submitted 2026-06-30 · 💻 cs.CV · cs.AI

Leveraging Phase Information to Boost Unrolled Network Learning for Image Deblurring

Samira Malek , Haichuan Zhang , Chul Lee , Vishal Monga This is my paper

Pith reviewed 2026-07-02 19:10 UTC · model grok-4.3

classification 💻 cs.CV cs.AI
keywords image deblurringphase estimationunrolled networksLMMSE estimatoramplitude phase decompositiondeep learningUPADNet
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The pith

Decomposing a blurred image into amplitude and phase, estimating both with LMMSE, then unrolling the recovery iterations into a trainable network produces sharper results than spatial-domain unrolling.

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

The paper starts from the observation that phase carries much of the detail needed to reverse blur. It builds separate linear minimum mean squared error estimators for the amplitude and phase of the observed blurred noisy image, then uses those estimates inside an iterative recovery procedure. The fixed matrices inside the iterations are replaced by learnable parameters, turning the whole procedure into an end-to-end trained network called UPADNet. Experiments on GoPro, RealBlur and COCO show the resulting network exceeds both conventional deep deblurrers and other unrolled networks, with the margin widening when noise rises or training examples become scarce.

Core claim

By first constructing LMMSE estimators for the amplitude and phase of the blurred observation and then unrolling the resulting iterative phase-amplitude recovery algorithm, the learned network UPADNet recovers the sharp image more accurately than networks that operate directly on the spatial image variable, with the advantage growing in high-noise and limited-data regimes.

What carries the argument

UPADNet, the network formed by unrolling each iteration of the phase-amplitude recovery algorithm and replacing its statistically fixed matrices with parameters trained on paired clean and degraded images.

If this is right

  • UPADNet records higher restoration metrics than prior deep networks on the GoPro, RealBlur, and COCO benchmarks.
  • The performance gap widens as input noise increases.
  • The performance gap also widens when the size of the training set is reduced.
  • Each layer of UPADNet corresponds to one iteration of the underlying phase-amplitude algorithm and is trained jointly.

Where Pith is reading between the lines

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

  • The same phase-aware unrolling pattern could be applied to related inverse problems such as image denoising or single-image super-resolution.
  • Extending the iteration to enforce consistency across video frames might yield a video deblurring variant without changing the core estimator design.
  • Because the LMMSE estimators are derived from signal statistics rather than hand-tuned priors, the method may transfer to new sensor noise characteristics with only modest retraining.

Load-bearing premise

That separating amplitude from phase and estimating the phase accurately is what drives the improvement over direct spatial-domain unrolling, especially when noise is high or training data is limited.

What would settle it

A controlled comparison in which a spatial-domain unrolled network trained on the same data matches or exceeds UPADNet on high-noise GoPro or RealBlur images would show that the phase decomposition is not the decisive factor.

Figures

Figures reproduced from arXiv: 2607.00251 by Chul Lee, Haichuan Zhang, Samira Malek, Vishal Monga.

Figure 1
Figure 1. Figure 1: Estimation of amplitude and phase components of the blurred observation. (a) Ground-truth sharp image. (b) Blurred observation generated by convolving the sharp image with a known kernel (bottom right of the blurred image) and addiing noise. (c) and (d) Comparison of the estimation errors of the naive and proposed LMMSE estimators for amplitude and phase on the test set. The proposed LMMSE estimators consi… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the proposed UPADNet architecture. (a) UPADBlock: one unrolled iteration derived from Algorithm 1, consisting of four sub-blocks that update AU , AH, θU , and θH with learnable parameters. (b) Weight Generator: dynamically produces iteration-specific weights {Wt i } 5 i=1 and filter Mt . (c) UPADNet: the complete multi￾scale network obtained by stacking multiple UPADBlocks with intermediate dow… view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative results on the GoPro dataset [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Qualitative results on the RealBlur-R dataset. performance on both RealBlur-R and RealBlur-J, attaining 41.29/0.979 and 34.35/0.946 (PSNR/SSIM), respectively. The consistent improvements across both synthetic (GoPro) and real-world datasets demonstrate strong generaliza￾tion capability. The performance gains on real data further suggest that the explicit Fourier-domain phase–amplitude decomposition enhance… view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative results on the RealBlur-J dataset [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Deblurred results on COCO with σ 2 = 0.05. Net maintains stable performance, demonstrating strong noise robustness. This robustness can be attributed to the structured phase–amplitude decomposition and the linear estimation-inspired updates [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Qualitative results on the COCO dataset with 60% of training data [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

While most image deblurring techniques directly restore the spatial image variable, we propose an amplitude and phase decomposition recognizing the importance of accurate phase estimation in recovering sharp image details. To that end, we first develop novel linear minimum mean squared (LMMSE) estimators of the amplitude and phase of the blurred, noisy image observation. An iterative optimization algorithm follows that recovers the sharp image using the aforementioned LMMSE estimators. Finally, matrix parameters that are statistically determined and fixed in the iterative algorithm are now learned using a training dataset of clean and degraded observations. Our deblurring engine is dubbed UPADNet (Unrolled Phase and Amplitude Decomposition Network), such that each iteration of the underlying phase and amplitude recovery algorithm is parameterized and trained end-to-end. Experiments over benchmark evaluation datasets such as GoPro, RealBlur and COCO datasets confirm that UPADNet outperforms state of the art deep networks including those based on algorithm unrolling in the image domain. The benefits of UPADNet are even more pronounced in high noise and limited training data regimes.

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

3 major / 1 minor

Summary. The paper claims that decomposing image deblurring into amplitude and phase components, deriving novel LMMSE estimators for the blurred noisy observation, unrolling an iterative recovery algorithm, and end-to-end learning of the matrix parameters yields UPADNet, which outperforms existing deep deblurring networks (including other unrolled methods) on GoPro, RealBlur, and COCO benchmarks, with larger gains under high noise and limited training data.

Significance. If the LMMSE phase estimators are rigorously derived and the empirical gains hold with proper controls, the work would strengthen the case for phase-aware unrolling in inverse problems, extending algorithm-unrolling literature by explicitly targeting phase recovery rather than operating directly in the spatial domain.

major comments (3)
  1. [Method (LMMSE estimators)] Method section on LMMSE estimators: no derivation of the amplitude or phase LMMSE estimators is supplied, so it is impossible to verify whether the phase estimator respects the circular topology of the argument (2π periodicity, branch-cut equivalence of +ε and −ε errors). If the estimator is simply arg of a complex-valued linear estimator, the claimed benefit reduces to standard complex-domain processing rather than a phase-specific advance.
  2. [Experiments] Experiments section: the abstract asserts benchmark outperformance and larger gains in high-noise/low-data regimes, yet the manuscript provides neither quantitative error bars, statistical significance tests, nor a description of training/evaluation protocols (data splits, noise levels, number of runs), leaving the central empirical claim unsupported.
  3. [Unrolling and training] Unrolling and training description: the paper states that matrix parameters are 'statistically determined and fixed' before being learned end-to-end, but supplies no analysis showing that the learned parameters remain independent of the training fit or that the unrolled network generalizes beyond the fitted distribution, undermining the low-data-regime claim.
minor comments (1)
  1. [Introduction / Method] Notation for amplitude and phase variables is introduced without an explicit forward model relating them to the observed blurred image; a single equation linking the decomposition to the degradation process would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment below and will revise the manuscript to strengthen the presentation of the LMMSE derivations, experimental protocols, and training analysis.

read point-by-point responses

  1. Referee: Method section on LMMSE estimators: no derivation of the amplitude or phase LMMSE estimators is supplied, so it is impossible to verify whether the phase estimator respects the circular topology of the argument (2π periodicity, branch-cut equivalence of +ε and −ε errors). If the estimator is simply arg of a complex-valued linear estimator, the claimed benefit reduces to standard complex-domain processing rather than a phase-specific advance.

    Authors: We acknowledge that the submitted manuscript did not include the explicit derivation of the amplitude and phase LMMSE estimators. In the revised version we will add the full derivation, starting from the complex observation model and arriving at the closed-form estimators for both amplitude and phase. The phase estimator is obtained by minimizing the mean-squared error on the phase variable after appropriate linearization around the circular manifold; we will explicitly show that it is not equivalent to taking the argument of a complex linear estimator and will discuss its handling of 2π periodicity and branch-cut equivalence. revision: yes

  2. Referee: Experiments section: the abstract asserts benchmark outperformance and larger gains in high-noise/low-data regimes, yet the manuscript provides neither quantitative error bars, statistical significance tests, nor a description of training/evaluation protocols (data splits, noise levels, number of runs), leaving the central empirical claim unsupported.

    Authors: We agree that the experimental reporting is incomplete. The revised manuscript will include (i) error bars computed over multiple independent training runs, (ii) statistical significance tests (paired t-tests or Wilcoxon tests) comparing UPADNet against the strongest baselines, and (iii) a detailed protocol section specifying data splits, exact noise variances, training-set sizes for the low-data experiments, and the number of runs performed. revision: yes

  3. Referee: Unrolling and training description: the paper states that matrix parameters are 'statistically determined and fixed' before being learned end-to-end, but supplies no analysis showing that the learned parameters remain independent of the training fit or that the unrolled network generalizes beyond the fitted distribution, undermining the low-data-regime claim.

    Authors: The parameters are initialized from closed-form statistical estimates derived from the observation model and are subsequently refined by end-to-end gradient descent. While the low-data experiments already demonstrate that the unrolled structure yields larger gains than purely data-driven baselines, we did not supply an explicit analysis of parameter sensitivity to the training distribution. In the revision we will add a short theoretical discussion of the separation between the model-based initialization and the learned corrections, together with an ablation that varies training-set size while keeping the statistical initialization fixed. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation uses standard LMMSE, iterative algorithm, and external end-to-end training

full rationale

The paper first states standard LMMSE estimators for amplitude and phase of the observation, derives an iterative recovery algorithm from them, and then unrolls the algorithm with learnable parameters trained end-to-end on external clean/degraded image pairs (GoPro, RealBlur, COCO). No equation reduces a reported prediction to a fitted quantity by construction, no self-citation supplies a load-bearing uniqueness theorem, and no ansatz is smuggled via prior work. Performance claims rest on empirical comparison to external benchmarks rather than internal re-labeling of fits.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

The approach rests on the premise that phase carries the dominant information for sharp detail recovery and that LMMSE estimators derived for the blurred observation remain useful when unrolled and trained; these premises are not independently verified in the abstract.

free parameters (1)
  • matrix parameters
    Parameters that were statistically determined and fixed in the iterative algorithm are now learned from the training dataset of clean and degraded observations.

pith-pipeline@v0.9.1-grok · 5720 in / 1277 out tokens · 37255 ms · 2026-07-02T19:10:15.965930+00:00 · methodology

discussion (0)

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