The beltway problem over orthogonal groups

• DOI: 10.48550/arxiv.2402.03787
• Publication Date: 2024-02-06
• Authors: Tamir Bendory; Dan Edidin; Oscar Mickelin
• Keywords: Signal Processing (eess.SP); 0301 basic medicine; FOS: Electrical engineering, electronic engineering, information engineering; 0102 computer and information sciences; Electrical Engineering and Systems Science - Signal Processing

The classical beltway problem entails recovering a set of points from their unordered pairwise distances on the circle. This can be viewed as special case crystallographic phase retrieval sparse signal its periodic autocorrelation. Based this interpretation, and motivated by cryo-electron microscopy, we suggest natural generalization to orthogonal groups: signal, up an transformation, autocorrelation over group. If support is collision-free, bound number solutions groups, prove that exactly one when radially collision-free (i.e., have distinct magnitudes). We also if products signal's weights are distinct, then determines uniquely, transformation. conclude paper considering binary signals show in case, condition need not sufficient determine