DEEPEN框架实现图像重建的高效采样与高精度估计
Deep End-to-End Posterior ENergy (DEEPEN) for image recovery
- 端到端学习后验能量函数，融合数据一致性与先验分布
- 在MAP估计上优于现有方法，采样速度比扩散模型快
- 无需算法展开或收缩约束，适应性强且计算开销小
当前端到端（E2E）和插件式（PnP）图像重建算法虽能近似最大后验（MAP）估计，却无法像扩散模型那样从后验分布中采样。而扩散模型又难以实现端到端训练。本文提出Deep End-to-End Posterior ENergy（DEEPEN）框架，同时支持MAP估计与后验采样。通过最大似然优化，端到端学习后验能量函数——即数据一致性误差与负对数先验分布之和。该方法无需算法展开，计算与内存开销更小；也无需传统PnP方法所需的收缩约束。实验表明，DEEPEN在MAP设置下性能超越现有E2E与PnP模型，采样速度显著快于扩散模型。此外，学习到的能量模型对成像条件变化更具鲁棒性。
原文摘要 · Abstract (English)
Current end-to-end (E2E) and plug-and-play (PnP) image reconstruction algorithms approximate the maximum a posteriori (MAP) estimate but cannot offer sampling from the posterior distribution, like diffusion models. By contrast, it is challenging for diffusion models to be trained in an E2E fashion. This paper introduces a Deep End-to-End Posterior ENergy (DEEPEN) framework, which enables MAP estimation as well as sampling. We learn the parameters of the posterior, which is the sum of the data consistency error and the negative log-prior distribution, using maximum likelihood optimization in an E2E fashion. The proposed approach does not require algorithm unrolling, and hence has a smaller computational and memory footprint than current E2E methods, while it does not require contraction constraints typically needed by current PnP methods. Our results demonstrate that DEEPEN offers improved performance than current E2E and PnP models in the MAP setting, while it also offers faster sampling compared to diffusion models. In addition, the learned energy-based model is observed to be more robust to changes in image acquisition settings.
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