Instance-Wise Adaptive Sampling for Dataset Construction in Approximating Inverse Problem Solutions
This work addresses the scalability and cost issues in inverse problem solving for fields like computational imaging or physics, though it is incremental as it builds on existing supervised learning approaches.
The authors tackled the problem of high data collection costs in learning-based inverse problem solutions by proposing an instance-wise adaptive sampling framework that dynamically allocates sampling effort based on specific test instances, resulting in significant gains in sample efficiency, especially with complex priors or high accuracy requirements.
We propose an instance-wise adaptive sampling framework for constructing compact and informative training datasets for supervised learning of inverse problem solutions. Typical learning-based approaches aim to learn a general-purpose inverse map from datasets drawn from a prior distribution, with the training process independent of the specific test instance. When the prior has a high intrinsic dimension or when high accuracy of the learned solution is required, a large number of training samples may be needed, resulting in substantial data collection costs. In contrast, our method dynamically allocates sampling effort based on the specific test instance, enabling significant gains in sample efficiency. By iteratively refining the training dataset conditioned on the latest prediction, the proposed strategy tailors the dataset to the geometry of the inverse map around each test instance. We demonstrate the effectiveness of our approach in the inverse scattering problem under two types of structured priors. Our results show that the advantage of the adaptive method becomes more pronounced in settings with more complex priors or higher accuracy requirements. While our experiments focus on a particular inverse problem, the adaptive sampling strategy is broadly applicable and readily extends to other inverse problems, offering a scalable and practical alternative to conventional fixed-dataset training regimes.