2025/04/27 by Gil Drozatz, Drozatz, Gil, Tamir Bendory +3
Computer Science · Engineering · #Advanced SAR Imaging Techniques #Direction-of-Arrival Estimation Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2504.19140
openalex publication_date 2025/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The multi-reference alignment (MRA) problem involves reconstructing a signal from multiple noisy observations, each transformed by a random group element. In this paper, we focus on the group \(SO(2)\) of in-plane rotations and propose two computationally efficient algorithms with theoretical guarantees for accurate signal recovery under a non-uniform distribution over the group. The first algorithm exploits the spectral properties of the second moment of the data, while the second utilizes the frequency marching principle. Both algorithms achieve the optimal estimation rate in high-noise regimes, marking a significant advancement in the development of computationally efficient and statistically optimal methods for estimation problems over groups.