Model-free estimation of the Cram\'er-Rao bound for deep-learning microscopy in complex media

TL;DR

This paper introduces a model-free method to estimate the Cramér-Rao bound for deep-learning microscopy in complex media, demonstrating that neural networks can approach fundamental precision limits in challenging imaging scenarios.

Contribution

It presents a novel, model-free approach to calculate the Cramér-Rao bound, enabling benchmarking of neural network performance in complex imaging tasks without requiring measurement of the transmission matrix.

Findings

Neural networks can nearly reach the theoretical precision limit in localizing targets behind scattering media.

The proposed method is broadly applicable for benchmarking deep-learning microscopy techniques.

Experimental results show convolutional networks approach the ultimate precision in dynamic scattering environments.

Abstract

Artificial neural networks have become important tools to harness the complexity of disordered or random photonic systems. Recent applications include the recovery of information from light that has been scrambled during propagation through a complex scattering medium, especially in the challenging case where the deterministic input-output transmission matrix cannot be measured. This naturally raises the question of what the limit is that information theory imposes on this recovery process, and whether neural networks can actually reach this limit. To answer these questions, we introduce a model-free approach to calculate the Cram\'er-Rao bound, which sets the ultimate precision limit at which artificial neural networks can operate. As an example, we apply this approach in a proof-of-principle experiment using laser light propagating through a disordered medium, evidencing that a convolutional network approaches the ultimate precision limit in the challenging task of localizing a reflective target hidden behind a dynamically-fluctuating scattering medium. The model-free method introduced here is generally applicable to benchmark the performance of any deep-learning microscope, to drive algorithmic developments and to push the precision of metrology and imaging techniques to their ultimate limit.