NON-UNIQUE GAMES OVER COMPACT GROUPS AND ORIENTATION ESTIMATION IN CRYO-EM.

Let be a compact group and let . We define the (NUG) problem as finding to minimize . We introduce a convex relaxation of the NUG problem to a (SDP) by taking the Fourier transform of over . The NUG framework can be seen as a generalization of the problem over the orthogonal group and the problem and includes many practically relevant problems, such as the to registering bandlimited functions over the unit sphere in -dimensions and orientation estimation of noisy cryo-Electron Microscopy (cryo-EM) projection images. We implement a SDP solver for the NUG cryo-EM problem using the alternating direction method of multipliers (ADMM). Numerical study with synthetic datasets indicate that while our ADMM solver is slower than existing methods, it can estimate the rotations more accurately, especially at low (SNR).