Trajectory Constraints for Imaging Inverse Problems
Quick Take
TRACE introduces a training-free framework for imaging inverse problems that stabilizes reconstruction paths by coupling adjacent states, enhancing reconstruction quality in both linear and nonlinear tasks. Stability analysis confirms that temporal coupling effectively bounds trajectory variation, leading to improved state transitions.
Key Points
- TRACE couples adjacent states for improved stability in imaging reconstructions.
- The framework is training-free, simplifying the reconstruction process.
- Stability analysis shows temporal coupling bounds trajectory variation.
- Experiments demonstrate enhanced reconstruction quality in various tasks.
- Trajectory-level analyses confirm the impact of temporal coupling on transitions.
Article Content
From source RSS / original summaryarXiv:2605. 29012v1 Announce Type: new 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.
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