用神经网络联合优化传感器位置和重建，提升逆问题的采样效率。
Neural Optimal Design of Experiment for Inverse Problems
- 联合训练神经重建模型与连续设计变量，单循环优化测量点位置。
- 在多项测试中重建精度优于基线方法，且无需额外稀疏性调节。
- 适合需要高效采样的逆问题场景，如医学成像与传感器部署。
我们提出神经最优实验设计（NODE），一种面向逆问题的基于学习的最优实验设计框架，避免传统双层优化和间接稀疏性正则化。NODE 在单一优化循环中联合训练神经重建模型与固定预算的连续设计变量（如传感器位置、采样时间或测量角度）。通过直接优化测量位置而非对密集候选集加权，该方法天然实现稀疏性，无需l1正则化调参，显著降低计算复杂度。我们在解析可解的指数增长基准、MNIST图像采样任务以及真实世界的稀疏视角X射线断层扫描案例中验证了其有效性。在所有场景中，NODE均优于基线方法，展现出更高的重建精度和任务特定性能。
原文摘要 · Abstract (English)
We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural reconstruction model and a fixed-budget set of continuous design variables representing sensor locations, sampling times, or measurement angles, within a single optimization loop. By optimizing measurement locations directly rather than weighting a dense grid of candidates, the proposed approach enforces sparsity by design, eliminates the need for l1 tuning, and substantially reduces computational complexity. We validate NODE on an analytically tractable exponential growth benchmark, on MNIST image sampling, and illustrate its effectiveness on a real world sparse view X ray CT example. In all cases, NODE outperforms baseline approaches, demonstrating improved reconstruction accuracy and task-specific performance.
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