Functional Multireference Alignment via Deconvolution
Abstract
Abstract. This paper studies the multireference alignment (MRA) problem of estimating a signal function from shifted, noisy observations. Our functional formulation reveals a new connection between MRA and deconvolution: the signal can be estimated from second-order statistics via Kotlarski’s formula, an important identification result in deconvolution with replicated measurements. To design our MRA algorithms, we extend Kotlarski’s formula to general dimension and study the estimation of signals with vanishing Fourier transform, thus also contributing to the deconvolution literature. We validate our deconvolution approach to MRA through both theory and numerical experiments.
Fields of Study & Subjects
Image Retrieval and Classification Techniques
Image Processing and 3D Reconstruction
Advanced Image and Video Retrieval Techniques
Publication details
- Journal / source
- SIAM Journal on Mathematics of Data Science
- Volume
- 8
- Issue
- 3
- Pages
- 920–945
- Publication date
- 18 August 2026
- Language
- EN