Signal Recovery under Non-Uniform Group Actions

Abstract:

Many modern scientific and engineering problems, such as single-particle cryo-electron microscopy (cryo-EM), involve recovering a signal from noisy observations acted on by unknown latent group transformations. A common approach assumes the underlying group distribution is uniform and applies methods such as maximum likelihood estimation (MLE) or the method of moments (MoM). In practice, however, this assumption is often violated due to experimental factors like preferred particle orientations or sample preparation artifacts. In this talk, I present a unified framework for understanding signal recovery under non-uniform latent group distributions. I discuss how non-uniformity affects statistical performance, optimization landscape, and computational design, highlighting the interplay between mathematical structure, inference, and algorithmic considerations. This perspective illustrates how insights from each domain inform and reinforce each other in data science problems.