Thomas D Grant's talk at the MIF++ seminar, https://kurlin.org/MIFplusplus.php

Speaker. Thomas D. Grant (SUNY University at Buffalo, US). Title. Information-Theoretic Approaches to the Inverse Problem in Solution Scattering. Abstract. Small-Angle X-ray Scattering (SAXS) provides a unique window into the structure of macromolecules in their native solution state. However, the spherical averaging inherent in the experiment creates an ill-posed inverse problem, where recovering a 3D structure from a 1D profile is mathematically non-unique. This talk explores a mathematical framework grounded in Shannon information theory to rigorously parameterize scattering data. By defining the scattering profile through a discrete set of intensities at Shannon sampling points, we can bridge the gap between reciprocal-space measurements and real-space structural parameters. This foundational approach allows for analytical regularization, error propagation, and the objective quantification of information content. We will discuss how these mathematical principles serve as the necessary foundation for robust structural modeling and the automated analysis of complex biological systems.