Nathan Soedjak

Yan Cheng, Yiwei Chen, Kui Ren et al.

This paper studies an inverse problem in nonlinear optical encryption. We examine chosen-plaintext attacks (CPA) on a nonlinear optical encryption strategy that integrates double random phase encryption (DRPE) into a nonlinear optical propagation model to enhance the security of the combined system. We first demonstrate that the system's phase information can be decoded from carefully designed differential CPA data. We then demonstrate that the strength of the optical device's nonlinearity can also be recovered from CPA data, indicating that including this parameter as an additional security key does not enhance protection against CPA attacks, although numerical simulations show that strong nonlinearity still poses significant challenges for CPA attacks. Finally, we provide a stability analysis to demonstrate that small errors in decoded security keys result in only small errors in the decrypted text, even though the encryption process is nonlinear.

Jiequn Han, Kui Ren, Nathan Soedjak

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.