Functional Multi-Reference Alignment via Deconvolution

2025/06/13 by Omar Ghattas, Al-Ghattas, Omar, Anna Little +4
Computer Science · #Advanced Image and Video Retrieval Techniques #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Image Processing and 3D Reconstruction #Image Retrieval and Classification Techniques #Information Theory (cs.IT) #Signal Processing (eess.SP) #Statistics Theory (math.ST) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2506.12201

openalex publication_date 2025/06/13 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

Abstract

This paper studies the multi-reference 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.

Citations

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Related

• Unbiasing Procedures for Scale-invariant Multi-reference Alignment
• Super-resolution multi-reference alignment
• Expectation-maximization for low-SNR multi-reference alignment
• Bispectrum Unbiasing for Dilation-Invariant Multi-reference Alignment
• Wavelet invariants for statistically robust multi-reference alignment