arXiv：cs.LG· Christian Tantardini, Stig Rune Jensen, Roberto Di Remigio Eik{\aa}s, Joakim Henrik Beck·· 7 小时前AI 评分27
Learned AMDI：用强化学习策略替代固定准则的自适应多分辨率扩散成像
Learned Adaptive Multiresolution Diffusion Imaging
AI 导读
研究提出 Learned Adaptive Multiresolution Diffusion Imaging（Learned AMDI），保留 AMDI 固定树传播器与层级约束，用 proximal policy optimization 训练的共享局部策略替代传播后的选择器。
正文
Abstract:Adaptive multiresolution methods reduce representation cost by concentrating fine-scale degrees of freedom where needed, but their tree updates are usually governed by fixed local criteria. We introduce Learned Adaptive Multiresolution Diffusion Imaging (Learned AMDI), which preserves the AMDI fixed-tree propagator and hierarchy constraints while replacing the post-propagation selector with a shared local policy trained by proximal policy optimization. Regression tests reproduce deterministic AMDI trajectories to machine precision when identical trees are used. In the Haar implementation studied here, the deterministic one-step selector accepts no refinements in 54 decisions. Across nine held-out cases, Learned AMDI executes 393 refinements and reduces the mean terminal reference discrepancy from $0.17496$ to $0.13657$, while occupancy rises from $0.13737$ to $0.26660$. Step-resolved diagnostics reveal occasional small adaptation-energy increases; fixed-tree energy stability therefore does not guarantee monotonicity of the learned outer iteration. At comparable occupancy, a validation-tuned observed-detail threshold reaches a discrepancy of $0.13792$ with slightly better RMSE and SSIM, placing both methods on essentially the same accuracy--occupancy tradeoff. A decision-1-only control reaches $0.13742$, indicating that most of the improvement on this static benchmark arises from the initial allocation. The shared actor transfers without retraining to $64\times64$ and $128\times128$ images, improving reference discrepancy, RMSE, and SSIM relative to deterministic AMDI, while the frozen threshold rule remains competitive. Learned AMDI thus provides a hierarchy-constrained, resolution-transferable mechanism for adaptive allocation and clarifies the contribution of sequential decisions.
| Subjects: | Numerical Analysis (math.NA); Machine Learning (cs.LG); Image and Video Processing (eess.IV) |
| Cite as: | arXiv:2610.07884 [math.NA] |
| (or arXiv:2610.07884v1 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2610.07884 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Christian Tantardini Prof. Dr. [view email]
[v1]
Tue, 6 Oct 2026 07:31:14 UTC (147 KB)
来源：arXiv：cs.LG · arxiv.org