Trajectory Constraints for Imaging Inverse Problems
This paper introduces TRACE, a training-free trajectory-constrained reconstruction framework that stabilizes the reconstruction path by coupling adjacent states, improving reconstruction quality for imaging inverse problems.
Article intelligence
Key points
- TRACE stabilizes reconstruction trajectories by coupling consecutive intermediate estimates.
- It models the reconstruction as a sequence of proximal updates approximated by neural networks.
- Stability analysis shows temporal coupling bounds trajectory variation.
- Experiments demonstrate improved quality on linear and nonlinear imaging tasks.
Why it matters
This matters because TRACE stabilizes reconstruction trajectories by coupling consecutive intermediate estimates.
Technical impact
May affect model selection, inference cost, product capability, and evaluation benchmarks.
[2605.29012] Trajectory Constraints for Imaging Inverse Problems
[Submitted on 27 May 2026]
Title:Trajectory Constraints for Imaging Inverse Problems
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Abstract:Diffusion-based and iterative methods have become effective tools for solving imaging inverse problems. Their reconstruction process naturally forms a trajectory of intermediate estimates. Although these intermediate estimates define a reconstruction trajectory, most methods do not explicitly regularize the transitions between consecutive states. To address this limitation, we introduce TRACE, a training-free TRAjectory-Constrained rEconstruction framework that stabilizes the reconstruction path by coupling adjacent states along the trajectory. This gives a trajectory-level model that can be interpreted as a sequence of proximal updates. Since the exact proximal update is generally intractable, we approximate it with a neural mapping. This yields a diffusion-like reconstruction process with an explicit coupling between neighboring states. We provide a stability analysis showing that temporal coupling bounds trajectory variation and that this control is preserved under untrained network updates. Experiments on linear and nonlinear image reconstruction tasks show that TRACE improves reconstruction quality. Trajectory-level analyses and ablations confirm that temporal coupling directly affects state transitions along the reconstruction path.
Comments: 20 pages, 10 figures
Subjects:
Computer Vision and Pattern Recognition (cs.CV)
Cite as: arXiv:2605.29012 [cs.CV]
(or arXiv:2605.29012v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2605.29012
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Chaoyan Huang [view email] [v1] Wed, 27 May 2026 19:08:44 UTC (37,974 KB)
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