Precision limits for parameter estimation in disordered media

¹ School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, United Kingdom
² Institute for Theoretical Physics, Vienna University of Technology (TU Wien), 1040 Vienna, Austria
³ Univ. Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France

^* e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 22 September 2025

Abstract

Artificial neural networks (ANNs) have emerged as powerful tools for imaging through complex scattering media, where conventional approaches fail due to dynamic and unpredictable light propagation. However, the fundamental limits of such ANN-based imaging systems remain largely unexplored. We present a model-free approach to estimate the Cramér-Rao bound (CRB), which sets the ultimate precision limit for parameter estimation, and apply it to evaluate the accuracy of the ANNs trained to image through complex scattering media. We compare how well various ANN architectures can localize a reflective target obscured by dynamic scattering. Our approach addresses high-dimensional, non-Gaussian, and correlated data using principal and independent component analysis combined with non-parametric density estimation. Comparing several ANN architectures, we find that convolutional networks with coordinate-aware layers can approach the CRB, achieving near-optimal localization performance. This method provides a general benchmarking tool to assess and guide the design of deep-learning-based imaging systems and opens opportunities for precision metrology in complex and disordered environments.