Group Symmetry Enables Faster Optimization in Inverse Problems

Junqi Tang; Guixian Xu

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arXiv · 2505.13223

Group Symmetry Enables Faster Optimization in Inverse Problems

Junqi Tang·Guixian Xu

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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.

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Junqi Tang, Guixian Xu. 2025-05-19. Group Symmetry Enables Faster Optimization in Inverse Problems. https://arxiv.org/abs/2505.13223

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