An adaptive variational model for multireference alignment with mixed noise

TL;DR

This paper introduces an adaptive variational model for multireference alignment that effectively handles mixed Gaussian noise, improving estimation accuracy in practical scenarios like cryo-EM.

Contribution

It develops a novel adaptive variational approach combining MAP and soft-max methods for MRA under mixed noise, with theoretical and numerical validation.

Findings

Outperforms existing methods with mixed noise

Proves existence of a minimizer for the model

Demonstrates robustness in numerical experiments

Abstract

Multireference alignment (MRA) problem is to estimate an underlying signal from a large number of noisy circularly-shifted observations. The existing methods are always proposed under the hypothesis of a single Gaussian noise. However, the hypothesis of a single-type noise is inefficient for solving practical problems like single particle cryo-EM. In this paper, We focus on the MRA problem under the assumption of Gaussian mixture noise. We derive an adaptive variational model by combining maximum a posteriori (MAP) estimation and soft-max method. There are two adaptive weights which are for detecting cyclical shifts and types of noise. Furthermore, we provide a statistical interpretation of our model by using expectation-maximization(EM) algorithm. The existence of a minimizer is mathematically proved. The numerical results show that the proposed model has a more impressive performance than the existing methods when one Gaussian noise is large and the other is small.