Sensor array and camera fusion via unbalanced optimal transport for 3D source localization

We address the problem of localizing multiple sources in 3D by combining sensor array measurements with camera observations. We propose a fusion framework extending the covariance matrix fitting method with an unbalanced optimal transport regularization term that softly aligns sensor array responses with visual priors while allowing flexibility in mass allocation. To solve the resulting largescale problem, we adopt a greedy coordinate descent algorithm that efficiently updates the transport plan. Its computational efficiency makes full 3D localization feasible in practice. The proposed framework is modular and does not rely on labeled data or training, in contrast with deep learning-based fusion approaches. Although validated here on acoustic arrays, the method is general to arbitrary sensor arrays. Experiments on real data show that the proposed approach improves localization accuracy compared to sensor-only baselines.

Convergence Guarantees for Unmixing PSFs over a Manifold with Non-Convex Optimization

The problem of recovering the parameters of a mixture of spike signals convolved with different PSFs is considered. Herein, the spike support is assumed to be known, while the PSFs lie on a manifold. A non-linear least squares estimator of the mixture parameters is formulated. In the absence of noise, a lower bound on the radius of the strong basin of attraction i.e., the region of convergence, is derived. Key to the analysis is the introduction of coherence and interference functions, which capture the conditioning of the PSF manifold in terms of the minimal separation of the support. Numerical experiments validate the theoretical findings. Finally, the practicality and efficacy of the non-linear least squares approach are showcased on spectral data from laser-induced breakdown spectroscopy.