2011/04/06 by Ronny Hadani, Amit Singer, Hadani, Ronny +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · Physics and Astronomy · #20G05 #Advanced Electron Microscopy Techniques and Applications #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Field-Flow Fractionation Techniques #Force Microscopy Techniques and Applications #Functional Analysis (math.FA) #Representation Theory (math.RT) #Spectral Theory (math.SP) #math.FA #math.RT #math.SP #msc:20G05
paper · pdf · doi:10.48550/arxiv.1104.1131
24 pages, 4 figures
arxiv created 2011/04/06 · openalex publication_date 2011/04/06 · arxiv updated 2011/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the formal algebraic structure underlying the intrinsic classification algorithm, recently introduced by Hadani, Shkolnisky, Singer and Zhao, for classifying noisy projection images of similar viewing directions in three-dimensional cryo-electron microscopy (cryo-EM). This preliminary classification is of fundamental importance in determining the three-dimensional structure of macromolecules from cryo-EM images. Inspecting this algebraic structure we obtain a conceptual explanation for the admissibility (correctness) of the algorithm and a proof of its numerical stability, thus putting it on firm mathematical grounds. The proof relies on studying the spectral properties of an integral operator of geometric origin on the two dimensional sphere, called the localized parallel transport operator. Along the way, we develop further the representation theoretic set-up for three-dimensional cryo-EM.