Stability of Constrained Optimization Models for Structured Signal Recovery

2026-01-08

arXiv.org

AI Summary

This study addresses the challenges of model stability and parameter tuning in the recovery of structured signals—such as sparse signals—from noisy measurements. It systematically investigates three constrained optimization models grounded in distinct structural priors. Through rigorous theoretical analysis, the work establishes a fundamental trade-off between sample complexity and mismatch error, and formally proves the robust stability of these models under both measurement noise and parameter perturbations. By incorporating structural priors like sparsity into regularized formulations, the proposed approach offers a principled framework that ensures both noise robustness and parameter stability, thereby providing strong theoretical guarantees for applications in imaging reconstruction, wireless communications, and related domains.

Technology Category

Reasoning under Uncertainty: Stochastic OptimizationMachine Learning: Structured LearningSearch and Optimization: Non-convex Optimization

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsUser Modeling, Personalization and Recommendation: User privacy protection in personalized systemsSecurity and Privacy: Large-scale security measurements

Abstract

Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the inherent problem stems from the prior knowledge about the signal's structure, such as sparsity which is critical for signal recovery models. We investigate three constrained optimization models that effectively address this challenge, each leveraging distinct forms of structural priors to regularize the solution space. Our theoretical analysis demonstrates that these models exhibit robustness to noise while maintaining stability with respect to tuning parameters that is a crucial property for practical applications, when the parameter selection is often nontrivial. By providing theoretical foundations, our work supports their practical use in scenarios where measurement imperfections and model uncertainties are unavoidable. Furthermore, under mild conditions, we establish tradeoff between the sample complexity and the mismatch error.

Problem

• structured signal recovery
• constrained optimization
• sparsity
• stability
• noise robustness

Innovation

• constrained optimization
• structured signal recovery
• robustness to noise
• parameter stability
• sample complexity