Group Symmetry Enables Faster Optimization in Inverse Problems

2025/05/19 by Junqi Tang, Guixian Xu, Tang, Junqi +1 · 1 citation
Computer Science · #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2505.13223

openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A Guide to Stochastic Optimisation for Large-Scale Inverse Problems
• Equivariant plug-and-play image reconstruction
• Practical Operator Sketching Framework for Accelerating Iterative Data-Driven Solutions in Inverse Problems
• Gradient Projection Iterative Sketch for Large-Scale Constrained Least-Squares
• Sharp Time--Data Tradeoffs for Linear Inverse Problems
• Proximal Splitting Methods in Signal Processing

Cited by

• Group-Theoretic Structure Governing Identifiability in Inverse Problems

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