Deep Neural-network Prior for Orbit Recovery from Method of Moments
This work addresses noise suppression in orbit recovery for applications like cryo-EM, but it is incremental as it builds on existing method of moments approaches by adding neural network priors.
The paper tackles orbit recovery problems, such as multireference alignment and cryo-EM, by using the method of moments with deep neural network priors to estimate signals and group element distributions from noisy observations. It demonstrates accelerated convergence for signal reconstruction and successfully reconstructs simulated and biological volumes in cryo-EM.
Orbit recovery problems are a class of problems that often arise in practice and various forms. In these problems, we aim to estimate an unknown function after being distorted by a group action and observed via a known operator. Typically, the observations are contaminated with a non-trivial level of noise. Two particular orbit recovery problems of interest in this paper are multireference alignment and single-particle cryo-EM modelling. In order to suppress the noise, we suggest using the method of moments approach for both problems while introducing deep neural network priors. In particular, our neural networks should output the signals and the distribution of group elements, with moments being the input. In the multireference alignment case, we demonstrate the advantage of using the NN to accelerate the convergence for the reconstruction of signals from the moments. Finally, we use our method to reconstruct simulated and biological volumes in the cryo-EM setting.