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arxiv: 2606.27086 · v1 · pith:2UZL5SLTnew · submitted 2026-06-25 · ⚛️ physics.comp-ph · physics.med-ph

GPU-accelerated superiorization on constrained physical problems with SupPy

Tobias Becher , Yair Censor , Kay Barshad , Niklas Wahl This is my paper

Pith reviewed 2026-06-26 01:57 UTC · model grok-4.3

classification ⚛️ physics.comp-ph physics.med-ph
keywords superiorizationfeasibility-seekingGPU accelerationseismic reconstructionlow-dose CTradiotherapy planningconstrained optimization
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The pith

Superiorization produces lower-noise images and lower-dose radiotherapy plans than feasibility-seeking alone, even on infeasible constraints.

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

The superiorization method occupies the space between plain feasibility-seeking and full constrained optimization by seeking feasible points whose objective function value is smaller, though not necessarily minimal. The authors created SupPy, an open modular Python package with CPU and GPU execution, and used it to superiorize algorithms for seismic image reconstruction, low-dose CT reconstruction, and intensity-modulated radiotherapy planning. In each of the three cases the superiorized runs improved on the corresponding feasibility-seeking runs. The imaging examples showed visibly less noise; the radiotherapy examples showed lower body dose and, notably, produced clinically usable plans when the full constraint set could not be satisfied simultaneously.

Core claim

When the superiorization method is applied through the SupPy toolbox, the resulting algorithms return feasible points with lower objective values than those obtained by feasibility-seeking alone; this yields reduced noise in seismic and CT reconstructions and reduced body dose in radiotherapy plans, and it produces clinically viable radiotherapy plans even when the underlying constraint set is infeasible.

What carries the argument

The superiorization method, which perturbs the iterates of a feasibility-seeking algorithm to decrease a chosen objective function while preserving feasibility.

If this is right

  • Seismic and CT images reconstructed with superiorization exhibit lower noise than those from feasibility-seeking alone.
  • Intensity-modulated radiotherapy plans from superiorization deliver lower dose to the body than those from feasibility-seeking alone.
  • Superiorization can return clinically viable radiotherapy plans when the full set of dose and geometry constraints is infeasible.
  • The open modular Python implementation with GPU support makes the method immediately usable on standard hardware for these physical problems.

Where Pith is reading between the lines

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

  • An open toolbox such as SupPy could make it straightforward to test superiorization on other inverse problems that currently rely only on feasibility-seeking or full optimization.
  • GPU execution opens the possibility of applying superiorization inside time-critical loops such as online adaptive radiotherapy or real-time seismic monitoring.
  • The ability to work with infeasible constraint sets may reduce the amount of manual constraint tuning required in clinical planning workflows.

Load-bearing premise

The measured gains in noise, dose, and viability on infeasible sets are caused by the superiorization perturbations themselves rather than by unstated choices in code or data handling inside SupPy.

What would settle it

An independent re-implementation of the same three superiorized algorithms that shows no consistent reduction in noise or dose relative to the corresponding feasibility-seeking versions.

Figures

Figures reproduced from arXiv: 2606.27086 by Kay Barshad, Niklas Wahl, Tobias Becher, Yair Censor.

Figure 1
Figure 1. Figure 1: Evolution of the relative errors for the different perturbation strategies [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Seismic reconstructions for clean data. Contours of the original tectonic plates are shown [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Seismic reconstructions for noisy data. Contours of the original image are shown in red. [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Evolution of relative error for different perturbation strategies. For each algorithm curves [PITH_FULL_IMAGE:figures/full_fig_p024_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The ground truth CT, the best reconstruction via feasibility-seeking only and its supe [PITH_FULL_IMAGE:figures/full_fig_p025_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Difference to the true solution for the reconstructions by feasibility-seeking and by [PITH_FULL_IMAGE:figures/full_fig_p026_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Evolution of the relative error for different perturbation strategies (explanation of the [PITH_FULL_IMAGE:figures/full_fig_p027_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: DVH comparison for the three different plan configurations of the horseshoe phantom. [PITH_FULL_IMAGE:figures/full_fig_p027_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Dose slices for a single fraction computed with feasibility-seeking and superiorization. [PITH_FULL_IMAGE:figures/full_fig_p028_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: DVH-comparison for the three different plan configurations of the Head and neck [PITH_FULL_IMAGE:figures/full_fig_p029_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of different plan slices for the head and neck patient. The top row shows [PITH_FULL_IMAGE:figures/full_fig_p030_11.png] view at source ↗
read the original abstract

The superiorization method (SM) is situated between feasibility-seeking and constrained optimization. Instead of aiming at the minimum of a given objective function over a constraint set, it seeks a feasible point at which the objective function value is reduced - though not necessarily minimal - rather than hard targets, or in which a mathematically optimal solution is not strictly required. While the method has been investigated for several applications in physics, its broader use has been limited, in part due to the lack of openly available software for researchers wishing to explore it. In this work we apply superiorization to three problems from applied physics: seismic image reconstruction, low-dose CT reconstruction and intensity-modulated radiotherapy treatment planning. These experiments are conducted with SupPy, an open-source modularized Python toolbox developed for this work, which supports execution of feasibility-seeking algorithms and their superiorized version on both the CPU and the GPU. In all three cases the superiorized algorithms achieve favorable results compared to feasibility-seeking alone, with reduced noise in the imaging examples and lowered body dose in the radiotherapy plans. For the radiotherapy case we further observe that superiorization produces clinically viable plans on infeasible constraint sets.

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 introduces SupPy, an open-source modular Python toolbox for feasibility-seeking and superiorization algorithms with CPU/GPU support, and applies it to three constrained problems in applied physics: seismic image reconstruction, low-dose CT reconstruction, and intensity-modulated radiotherapy (IMRT) treatment planning. It claims that in all cases the superiorized versions produce favorable outcomes relative to feasibility-seeking alone (reduced noise in imaging; lowered body dose in radiotherapy) and that superiorization yields clinically viable plans even on infeasible constraint sets.

Significance. If the empirical claims hold with proper controls, the work supplies a reusable, GPU-accelerated implementation of an established method (superiorization) that sits between feasibility-seeking and constrained optimization. The open modular toolbox itself is a concrete contribution that could lower the barrier for physicists to test superiorization on new problems; the radiotherapy observation on infeasible sets, if quantified, would be a practically relevant demonstration.

major comments (2)
  1. [Abstract, §§3–5] Abstract and §3–5 (results sections): the central claim that superiorized algorithms achieve 'favorable results' (reduced noise, lowered dose, viable plans on infeasible sets) is stated without any quantitative metrics, error bars, baseline iteration counts, stopping criteria, or explicit definitions of the objective functions and infeasibility measures. This prevents verification that the reported gains are produced by the superiorization perturbations rather than by unstated differences in implementation, data handling, or GPU kernels between SupPy and the feasibility-seeking baselines.
  2. [§2, §4] §2 (SupPy description) and §4 (radiotherapy experiments): no explicit statement that the feasibility-seeking and superiorized runs use identical iteration budgets, identical constraint operators, and identical GPU kernels. Without this control, the attribution of improvements to the superiorization method (as opposed to modular implementation choices) cannot be assessed.
minor comments (2)
  1. [Abstract, §1] The abstract and introduction would benefit from a short table or bullet list summarizing the three test problems, the constraint sets, and the objective functions being reduced.
  2. [Figures 2–5] Figure captions and axis labels in the imaging and dose-volume results should explicitly state the quantitative improvement (e.g., noise standard deviation or mean body dose) rather than relying on visual comparison alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help strengthen the clarity and verifiability of our claims. We address each major point below and will incorporate the requested details in a revised manuscript.

read point-by-point responses

  1. Referee: [Abstract, §§3–5] Abstract and §3–5 (results sections): the central claim that superiorized algorithms achieve 'favorable results' (reduced noise, lowered dose, viable plans on infeasible sets) is stated without any quantitative metrics, error bars, baseline iteration counts, stopping criteria, or explicit definitions of the objective functions and infeasibility measures. This prevents verification that the reported gains are produced by the superiorization perturbations rather than by unstated differences in implementation, data handling, or GPU kernels between SupPy and the feasibility-seeking baselines.

    Authors: We agree that quantitative support is necessary to substantiate the claims and enable verification. In the revised manuscript we will augment the abstract and §§3–5 with explicit numerical metrics (e.g., noise-reduction percentages or RMSE values with standard deviations where repeated runs permit, mean body-dose reductions, and feasibility-gap measures), iteration budgets, stopping criteria, and precise definitions of the objective functions and infeasibility measures used in each experiment. These additions will make clear that the reported improvements arise from the superiorization perturbations rather than implementation differences. revision: yes

  2. Referee: [§2, §4] §2 (SupPy description) and §4 (radiotherapy experiments): no explicit statement that the feasibility-seeking and superiorized runs use identical iteration budgets, identical constraint operators, and identical GPU kernels. Without this control, the attribution of improvements to the superiorization method (as opposed to modular implementation choices) cannot be assessed.

    Authors: We accept that an explicit control statement is required. The SupPy implementation already enforces identical iteration budgets, constraint operators, and GPU kernels for paired feasibility-seeking and superiorized runs, differing only by the addition of the superiorization perturbation step. In the revised §2 and §4 we will insert a dedicated paragraph documenting these identical controls and confirming that the only algorithmic difference is the superiorization perturbation itself. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical application of established method

full rationale

The paper applies the pre-existing superiorization method (SM) to three physics problems via new open-source software SupPy. The abstract and provided text contain no derivations, equations, fitted parameters, or predictions that reduce to inputs by construction. Results are empirical comparisons of superiorized vs. feasibility-seeking runs; the central claims rest on observed outcomes rather than any self-referential definition or self-citation chain that would force the reported improvements. This is a standard non-circular empirical software/application paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the established definition of the superiorization method and on the assumption that the new software correctly implements it for the chosen problems.

axioms (1)
  • domain assumption Superiorization seeks a feasible point with reduced objective value rather than a mathematically optimal solution.
    Stated directly in the abstract as the positioning of SM between feasibility-seeking and constrained optimization.

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discussion (0)

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Reference graph

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