An accelerated expectation-maximization algorithm for multi-reference alignment
This addresses computational efficiency for image reconstruction in high-noise scenarios, though it is incremental as it builds on existing EM methods.
The authors tackled the multi-reference alignment problem of estimating an image from noisy, rotated copies by proposing Synch-EM, a framework combining angular synchronization and expectation-maximization, which accelerated EM by orders of magnitude in high noise without degrading reconstruction quality.
The multi-reference alignment (MRA) problem entails estimating an image from multiple noisy and rotated copies of itself. If the noise level is low, one can reconstruct the image by estimating the missing rotations, aligning the images, and averaging out the noise. While accurate rotation estimation is impossible if the noise level is high, the rotations can still be approximated, and thus can provide indispensable information. In particular, learning the approximation error can be harnessed for efficient image estimation. In this paper, we propose a new computational framework, called Synch-EM, that consists of angular synchronization followed by expectation-maximization (EM). The synchronization step results in a concentrated distribution of rotations; this distribution is learned and then incorporated into the EM as a Bayesian prior. The learned distribution also dramatically reduces the search space, and thus the computational load, of the EM iterations. We show by extensive numerical experiments that the proposed framework can significantly accelerate EM for MRA in high noise levels, occasionally by a few orders of magnitude, without degrading the reconstruction quality.