Trajectory Constraints for Imaging Inverse Problems

2026-05-27

AI Summary

This work addresses the instability of reconstruction trajectories in existing methods for solving imaging inverse problems, which stems from the lack of explicit regularization on intermediate state transitions. The authors propose TRACE, a novel framework that introduces trajectory-level constraints for the first time in this domain. By incorporating a temporal coupling mechanism, TRACE explicitly models dependencies between consecutive reconstruction states, formulating the entire process as a sequence of proximal updates. A neural mapping is employed to approximate these updates without requiring additional training. This approach stabilizes the reconstruction path in a training-free manner and significantly improves image quality in both linear and nonlinear reconstruction tasks. Trajectory analysis and ablation studies confirm that temporal coupling effectively governs state transitions throughout the reconstruction process.

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.

Problem

• trajectory constraints
• imaging inverse problems
• reconstruction trajectory
• temporal coupling
• state transitions

Innovation

• trajectory constraints
• imaging inverse problems
• proximal updates
• temporal coupling
• diffusion-based reconstruction