This repository contains the scripts Gen_Fig1, Gen_Fig2a, and Gen_Fig3 to reproduce the figures in the paper "SPARSE MULTI-REFERENCE ALIGNMENT: SAMPLE COMPLEXITY AND COMPUTATIONAL HARDNESS" by Tamir Bendory, Oscar Mickelin, and Amit Singer. It also contains auxiliary functions that are needed to implement the expectation-maximization, bispectrum inversion, and semidefinite programming (SDP) algorithms.
The SDP requires CVX http://cvxr.com/ to be installed. The bispectrum requires manopt https://www.manopt.org/ to be installed. The SoS requires Yalmip (https://yalmip.github.io/) and Gloptipoly3 (https://homepages.laas.fr/henrion/software/gloptipoly/) to be installed.