2021/07/22 by Cuicui Zhao, Jun Liu, Zhao, Cuicui +3
Engineering · Environmental Science · #00-01 #60G35 #FOS: Mathematics #G.m #Optimization and Control (math.OC) #Soil Geostatistics and Mapping #Structural Health Monitoring Techniques #Synthetic Aperture Radar (SAR) Applications and Techniques
paper · pdf · doi:10.48550/arxiv.2107.10425
openalex publication_date 2021/07/22 · openalex created_date 2021/08/02 · openalex updated_date 2026/07/28
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.