This research addresses the challenge of regularization parameter selection in random source reconstruction, proposing a framework integrating a generalized SURE, random discrepancy principle, and a hybrid Bayesian-frequentist approach, providing theoretical analysis and numerical validation.
Key findings
Proposes a generalized Stein’s Unbiased Risk Estimate (SURE) adapted for stochastic forward operators.
Introduces a random discrepancy principle that incorporates source uncertainty.
Develops a hybrid Bayesian-frequentist approach leveraging source covariance structure.
Theoretical analysis establishes consistency and convergence rates under standard source conditions.
Limitations & open questions
The framework's performance in real-world applications with non-Gaussian noise is not discussed.
The theoretical analysis assumes standard source conditions, which may not hold in all practical scenarios.