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arxiv: 2606.24567 · v1 · pith:J3PGI4W5new · submitted 2026-06-23 · 💻 cs.CV · physics.med-ph

Multilevel Stochastic Plug-and-Play for Sparse-View CT Reconstruction

Antoine De Paepe , Alexandre Bousse , Dimitris Visvikis This is my paper

Pith reviewed 2026-06-26 00:31 UTC · model grok-4.3

classification 💻 cs.CV physics.med-ph
keywords Sparse-view CTPlug-and-PlayMultilevel methodsStochastic optimizationWavelet decompositionImage reconstructionPrior coherenceMultiresolution analysis
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The pith

Multilevel stochastic Plug-and-Play reconstructs sparse-view CT images at speeds comparable to state-of-the-art while matching their quality.

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

The paper introduces a multilevel extension of stochastic Plug-and-Play for sparse-view CT reconstruction. Standard stochastic PnP improves robustness by re-noising but requires many iterations to converge. The new method performs its multilevel updates inside multiresolution analysis approximation spaces. Because of the wavelet decomposition structure the expected prior-coherence correction term becomes zero, so the algorithm avoids repeated fine-scale denoiser evaluations that would otherwise dominate the cost. Experiments show the resulting ML-SPnP procedure delivers reconstruction quality on par with existing methods yet runs substantially faster.

Core claim

In the stochastic Plug-and-Play setting, enforcing prior coherence across resolution levels normally demands multiple fine-scale denoiser calls to estimate the required gradient corrections. When the multilevel steps are executed inside the approximation spaces of a multiresolution analysis, the structure of the wavelet decomposition makes the prior-coherence correction vanish in expectation. This property removes the need to compute those expensive fine-level stochastic prior gradients for the coarse-level updates, yielding an accelerated reconstruction algorithm whose output quality remains comparable to single-level stochastic PnP on sparse-view CT data.

What carries the argument

Multilevel stochastic Plug-and-Play (ML-SPnP) executed in multiresolution analysis approximation spaces, where the wavelet decomposition structure makes the prior-coherence correction vanish in expectation.

If this is right

  • ML-SPnP produces SVCT reconstructions of quality comparable to state-of-the-art single-level stochastic PnP.
  • Runtime is substantially lower because fine-level stochastic prior gradients need not be estimated for coarse corrections.
  • The acceleration is obtained by restricting multilevel steps to MRA approximation spaces.
  • The method inherits the robustness properties of stochastic PnP while inheriting the speed of multilevel schemes.

Where Pith is reading between the lines

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

  • The same vanishing-expectation property could be tested in other inverse problems that already use stochastic PnP, such as limited-angle tomography or MRI.
  • If the result holds for additional wavelet families, deeper multilevel hierarchies become feasible without linear cost growth.
  • Faster per-iteration times might allow the method to be embedded inside real-time or adaptive acquisition protocols for low-dose CT.
  • The approach leaves open whether similar expectation cancellations exist for non-wavelet multiresolution bases.

Load-bearing premise

The structure of the wavelet decomposition causes the prior-coherence correction to vanish in expectation.

What would settle it

Measure the expected value of the prior-coherence correction term on SVCT data using the chosen wavelet family; if the expectation is not statistically indistinguishable from zero, the runtime saving disappears.

Figures

Figures reproduced from arXiv: 2606.24567 by Alexandre Bousse, Antoine De Paepe, Dimitris Visvikis.

Figure 1
Figure 1. Figure 1: Qualitative comparison on sparse-view CT reconstruction with [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Qualitative comparison on sparse-view CT reconstruction with [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effect of the NFE used to estimate the stochastic [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of annealing procedure on ML-SPnP across mul [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Mean reconstruction quality over elapsed time for 20-view CT on the Lymph Nodes dataset. Curves show PSNR, SSIM, [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Mean reconstruction quality over elapsed time for 40-view CT on the head CQ500 dataset. Curves show PSNR, SSIM, [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

Sparse-view computed tomography (SVCT) reduces radiation exposure and acquisition time, but the limited number of projection views makes the reconstruction problem severely ill-posed and leads to streak artifacts when analytical methods are used. Plug-and-Play (PnP) methods provide an effective way to combine data fidelity with learned image priors, while stochastic PnP methods further improve robustness by matching the denoiser input distribution through re-noising. However, these methods often require many iterations to converge, which limits their practical efficiency. In this work, we propose a multilevel (ML) stochastic PnP method for SVCT that accelerates stochastic PnP reconstruction. We highlight that, in the stochastic setting, directly enforcing prior coherence across levels would require accurately estimating fine-level prior gradients through multiple denoiser function evaluations, which substantially increases the computational cost. Motivated by this observation, we perform the multilevel steps in multiresolution analysis (MRA) approximation spaces. This choice is supported by the structure of the wavelet decomposition, which causes the prior-coherence correction to vanish in expectation, thereby avoiding costly estimation of fine-level stochastic prior gradients for the coarse-level corrections. Experiments on SVCT reconstruction show that our method, called Multilevel Stochastic Plug-and-Play (ML-SPnP), achieves reconstruction quality comparable to state-of-the-art methods while substantially reducing runtime.

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

1 major / 1 minor

Summary. The paper proposes Multilevel Stochastic Plug-and-Play (ML-SPnP) for sparse-view CT (SVCT) reconstruction. It performs multilevel corrections within multiresolution analysis (MRA) approximation spaces, asserting that the structure of the wavelet decomposition causes the prior-coherence correction term to vanish in expectation. This is claimed to avoid repeated fine-level stochastic denoiser evaluations required for prior-coherence enforcement. Experiments are said to show reconstruction quality comparable to state-of-the-art methods with substantially reduced runtime.

Significance. If the vanishing-in-expectation property holds for the chosen stochastic PnP noise model, denoiser, and wavelet family, and if the runtime/quality claims are substantiated with quantitative evidence, the approach would offer a structurally motivated way to accelerate stochastic PnP iterations for ill-posed inverse problems without additional per-iteration cost. This could be relevant for practical deployment of learned-prior methods in CT.

major comments (1)
  1. [Abstract] Abstract: The runtime-reduction claim rests on the assertion that 'the structure of the wavelet decomposition... causes the prior-coherence correction to vanish in expectation.' No derivation, explicit expectation calculation, or numerical verification is referenced for the specific stochastic PnP noise model and wavelet family. If this expectation is not exactly zero, the claimed computational saving does not materialize and the method reverts to the cost it seeks to avoid.
minor comments (1)
  1. [Abstract] Abstract: Experimental claims are stated without any quantitative metrics (e.g., PSNR/SSIM), dataset descriptions, baseline methods, or runtime numbers, making the 'comparable quality... substantially reducing runtime' statement impossible to assess from the given text.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and constructive feedback on our manuscript. We address the major comment point-by-point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The runtime-reduction claim rests on the assertion that 'the structure of the wavelet decomposition... causes the prior-coherence correction to vanish in expectation.' No derivation, explicit expectation calculation, or numerical verification is referenced for the specific stochastic PnP noise model and wavelet family. If this expectation is not exactly zero, the claimed computational saving does not materialize and the method reverts to the cost it seeks to avoid.

    Authors: We agree that the abstract would benefit from an explicit pointer to the supporting analysis. In the revised version we will expand the relevant paragraph in Section 3 to include the full expectation calculation: under the orthogonal wavelet decomposition and the zero-mean stochastic noise model used in the PnP iteration, the cross-term between the prior-coherence correction and the detail coefficients integrates to zero by construction of the MRA approximation spaces. We will also add a short numerical check (Monte-Carlo estimate of the expectation on a held-out phantom) in the supplementary material to confirm the property holds for the specific denoiser and wavelet family employed. revision: yes

Circularity Check

0 steps flagged

No circularity: efficiency claim rests on asserted wavelet property, not self-referential reduction

full rationale

The abstract presents the runtime reduction as following from the wavelet decomposition structure causing prior-coherence correction to vanish in expectation. This is framed as a direct consequence of MRA properties rather than a fitted parameter, self-citation chain, or definition that loops back to the method's own outputs. No equations, derivations, or self-citations are exhibited that would make any prediction equivalent to its inputs by construction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the wavelet decomposition property that prior-coherence corrections vanish in expectation; this is treated as a domain assumption rather than derived.

axioms (1)
  • domain assumption Wavelet decomposition structure causes the prior-coherence correction to vanish in expectation
    Invoked to justify performing multilevel steps in MRA spaces and avoid fine-level gradient estimation.

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Reference graph

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