Likelihood landscape and maximum likelihood estimation for the discrete orbit recovery model

• Published in: Communications on pure and applied mathematics Vol. 76; no. 6; pp. 1208 - 1302
• Main Authors: Fan, Zhou, Sun, Yi, Wang, Tianhao, Wu, Yihong
• Format: Journal Article
• Language: English
• Published: Melbourne John Wiley & Sons Australia, Ltd 01.06.2023; John Wiley and Sons, Limited
• Subjects: Algorithms; Eigenvalues; Fisher information; Group theory; Image processing; Low noise; Maximum likelihood estimation; Normal distribution; Optimization; Permutations; Polynomials; Probabilistic models; Random noise; Recovery; Saddle points; Statistical analysis; Statistical models

We study the nonconvex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This is a statistical model motivated by applications in molecular microscopy and image processing, where each measurement of an unknown object is subject to an i...