用分数模型先验加速图像重建，收敛更快且质量更高。
Provably Accelerated Imaging with Restarted Inertia and Score-based Image Priors
- 引入重启惯性机制提升收敛速度
- 理论证明比传统方法更快达到稳定点
- 适合需要快速高质量重建的成像任务
快速收敛与高质量图像恢复是求解病态成像逆问题算法的两大关键。现有方法如基于去噪的正则化（RED）通常专注于设计复杂的图像先验以提升重建质量，而将收敛加速交给启发式策略。为此，我们提出重启惯性结合分数模型先验（RISP），作为RED的严格扩展。RISP引入重启惯性以实现快速收敛，同时保留分数模型先验以保证重建质量。我们证明RISP在不依赖图像先验凸性的情况下，可获得比RED更快的驻点收敛速率。进一步，我们推导并分析了其对应的连续时间动力系统，揭示了RISP与重球常微分方程（ODE）之间的联系。在多种成像逆问题上的实验表明，RISP能在实现快速收敛的同时，获得高质量重建结果。
原文摘要 · Abstract (English)
Fast convergence and high-quality image recovery are two essential features of algorithms for solving ill-posed imaging inverse problems. Existing methods, such as regularization by denoising (RED), often focus on designing sophisticated image priors to improve reconstruction quality, while leaving convergence acceleration to heuristics. To bridge the gap, we propose Restarted Inertia with Score-based Priors (RISP) as a principled extension of RED. RISP incorporates a restarting inertia for fast convergence, while still allowing score-based image priors for high-quality reconstruction. We prove that RISP attains a faster stationary-point convergence rate than RED, without requiring the convexity of the image prior. We further derive and analyze the associated continuous-time dynamical system, offering insight into the connection between RISP and the heavy-ball ordinary differential equation (ODE). Experiments across a range of imaging inverse problems demonstrate that RISP enables fast convergence while achieving high-quality reconstructions.
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