A promising way to mitigate the expensive process of obtaining a high-dimensional signal is to acquire a limited number of low-dimensional measurements and solve an under-determined inverse problem by utilizing the structural prior about the signal. In this paper, we focus on adaptive acquisition schemes to save further the number of measurements. To this end, we propose a reinforcement learning-based approach that sequentially collects measurements to better recover the underlying signal by acquiring fewer measurements. Our approach applies to general inverse problems with continuous action spaces and jointly learns the recovery algorithm. Using insights obtained from theoretical analysis, we also provide a probabilistic design for our methods using variational formulation. We evaluate our approach on multiple datasets and with two measurement spaces (Gaussian, Radon). Our results confirm the benefits of adaptive strategies in low-acquisition horizon settings.

翻译：缓解获取高维信号昂贵过程的一种有效途径是采集有限数量的低维测量值，并利用信号的结构先验信息求解欠定逆问题。本文聚焦于自适应采集方案，以进一步减少所需测量数量。为此，我们提出一种基于强化学习的方法，该方法通过顺序采集测量值，以更少的测量数据实现更优的底层信号重建。我们的方法适用于具有连续动作空间的通用逆问题，并能联合学习重建算法。基于理论分析获得的启示，我们还通过变分框架为方法提供了概率化设计。我们在多个数据集和两种测量空间（高斯、拉东）上评估了所提方法。实验结果证实了自适应策略在低采集量场景下的优势。