提出首个无需调参的PDHG优化方法，提升图像重建稳定性
A Relaxed Primal-Dual Hybrid Gradient Method with Line Search
- 结合两种线搜索策略，自动确定步长与松弛参数
- 在多个图像重建任务中表现稳定，包括新型MRI逆问题
- 首次实现完全免调参的PDHG，适合工程落地
原始的增广拉格朗日型对偶混合梯度法（PDHG）在图像重建等优化问题中表现良好，但通常需要手动设置三个超参数，且算法性能对参数敏感。为实现无需调参的算法，本文结合了两种现有线搜索：其一由Malitsky等人提出，用于调整迭代中的两个步长；其二基于PDHG与Douglas-Rachford分裂法对偶形式的联系，构建了针对松弛参数的线搜索。实验表明，该组合线搜索在多个问题上均有效，包括一个新颖的磁共振成像（MRI）逆问题。本文提出的算法是首个在所有数值实验中均无需调整线搜索超参数的参数自由型PDHG变体。
原文摘要 · Abstract (English)
The primal-dual hybrid gradient method (PDHG) is useful for optimization problems that commonly appear in image reconstruction. A downside of PDHG is that there are typically three user-set parameters and performance of the algorithm is sensitive to their values. Toward a parameter-free algorithm, we combine two existing line searches. The first, by Malitsky et al., is over two of the step sizes in the PDHG iterations. We then use the connection between PDHG and the primal-dual form of Douglas-Rachford splitting to construct a line search over the relaxation parameter. We demonstrate the efficacy of the combined line search on multiple problems, including a novel inverse problem in magnetic resonance image reconstruction. The method presented in this manuscript is the first parameter-free variant of PDHG (across all numerical experiments, there were no changes to line search hyperparameters).
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