Jiaying Jia | Searcharxiv

arXiv2026

Dual-Filtration Topology Recovery from Qualitative Acoustic Scattering Indicators

Qualitative inverse scattering methods produce gray-scale indicator fields, from which the topology of the scatterer must be inferred without a prescribed threshold. We propose a dual-filtration method that estimates the component and cavity structure directly from the indicator. Superlevel sets are used to recover the exterior components, while sublevel persistent homology identifies interior cavities associated with the reconstructed envelope. The two types of information are combined into a binary reconstruction, allowing different topological features to be resolved at different intensity levels. We establish geometric and stability results that characterize when the topology can be reliably detected. Full-wave Lippmann--Schwinger experiments with factorization-method indicators show accurate recovery for well-resolved configurations and clear resolution transitions as component separation and cavity size vary.

math.NA↗

arXiv2026

A Bayesian approach with persistent homology prior for Robin coefficient identification in a parabolic problem

The reconstruction of time-dependent Robin coefficients is a challenging inverse heat transfer problem due to its inherent ill-posedness. This paper introduces a hierarchical Bayesian approach integrated with a persistent homology (PH) prior for robust coefficient estimation. By quantifying the birth and death of topological features, the PH-based prior provides a global structural constraint that transcends local derivative based penalties. Numerical experiments show that this topological perspective allows for the preservation of complex temporal profiles without the typical staircase distortions of total variation (TV) priors or the excessive blurring of Gaussian models. A key feature of our framework is the hierarchical implementation, which yields an automated, data-driven selection of hyperparameters. The results demonstrate that while PH-based inference yields competitive accuracy compared to TV regularization, it offers superior performance in preserving the multiscale characteristics of the Robin coefficient, providing a robust alternative for convective heat transfer diagnostics

stat.CO↗