This paper introduces a new approach for solving stochastic inverse problems with correlated measurement errors, integrating topological gradient methods with a Bayesian framework to model noise covariance, providing superior reconstruction accuracy and uncertainty calibration.
Key findings
Derives stochastic topological gradient for quadratic misfit functionals with arbitrary covariance structures.
Proposes a hybrid algorithm combining topological gradient descent with Bayesian uncertainty quantification.
Establishes convergence guarantees under suitable regularity conditions.
Validates the approach on EIT and DOT problems, demonstrating superior performance over methods ignoring error correlations.
Limitations & open questions
The extension to stochastic inverse problems with correlated errors remains largely unexplored.