Parameter estimation in disordered media

Abstract

This thesis investigates the information content in speckle patterns, with a focus on the role of ballistic photons and the applicability of Fisher information as a benchmark for machine learning models. We begin by analyzing experimental data to understand deviations in the probability distribution function caused by ballistic photons and other contributing factors. Building on this, we simulate fully developed speckles, both with and without correlations. We then derive and assess the Fisher information for uncorrelated speckles, explore the effects of noise, and demonstrate how sufficient sampling can mitigate it. A key part of the work involves evaluating the use of a UNet-based machine learning model, where an End-to-End approach proved superior in performance and efficiency. Finally, we show that Fisher information can reliably predict the lower bound of model variance in uncorrelated cases, though it should be complemented with bias analysis. The study identifies the sensitivity of Fisher information to derivative estimation as a significant challenge, especially for real-world applications. It also raises questions about the relative contributions of ballistic photons and speckle correlations to the overall information content, pointing toward future work that will address these issues using more generalized frameworks.