图像去模糊中凸优化方法的多级预处理策略
Multilevel Preconditioning Strategies for Convex Optimization Methods in Image Deblurring
AI总结：
研究图像去模糊中凸优化方法，结合预处理和多级策略为正则化凸优化问题的算法设计加速框架，经图像去模糊数值实验验证，该方法相比标准方法在收敛速度上有显著提升。
AI中文摘要：
近端梯度方法在成像中广泛应用，结合可变度量和/或外推步骤可加速其收敛。近期研究表明预处理策略能显著增强这种加速效果，特别是对于图像去模糊问题。同时，已引入多级框架来加速图像恢复问题的惯性和不精确前向 - 后向算法。本文结合预处理和多级策略，为正则化凸优化问题的标准和不精确前向 - 后向算法设计了一个稳健且一致的加速框架。图像去模糊的数值实验证实，与标准方法相比，我们的方法在收敛速度上有显著提升。
英文摘要：
Proximal gradient methods are widely used in imaging, and their speed of convergence can be accelerated by incorporating variable metrics and/or extrapolation steps. Recent works have shown that preconditioning strategies can significantly enhance this acceleration, in particular, for image deblurring problems. In parallel, a multilevel framework has been introduced to speed up inertial and inexact forward-backward schemes for image restoration problems. In this paper, we combine preconditioning and multilevel strategies to design a robust and consistent acceleration framework for both standard and inexact forward-backward schemes applied to regularized convex optimization problems. Numerical experiments in image deblurring confirm that our approach yields a substantial improvement in convergence speed compared to standard methods.
