Group Symmetry Enables Faster Optimization in Inverse Problems
Optimization and Control
2025-05-21 v2
Abstract
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the existence of a special class of structure-adaptive optimization algorithms which are tailored for symmetry-structured inverse problems such as CT/MRI/PET, compressed sensing, and image processing applications such as inpainting/deconvolution, etc.
Cite
@article{arxiv.2505.13223,
title = {Group Symmetry Enables Faster Optimization in Inverse Problems},
author = {Junqi Tang and Guixian Xu},
journal= {arXiv preprint arXiv:2505.13223},
year = {2025}
}