Joint Bayesian estimation of close subspaces from noisy measurements
This work addresses a specific problem in signal processing for researchers analyzing subspace distances, but it is incremental as it builds on existing Bayesian and Procrustes-related methods.
The paper tackles the problem of estimating the distance between two noisy subspace signals by analyzing the angles between them, using a Bayesian approach with a joint prior distribution to adjust subspace closeness, and shows that the new schemes provide more accurate angle estimates compared to singular value decomposition-based methods.
In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue reminiscent of the well-known Procrustes problem. A Bayesian approach is investigated where the subspaces of interest are considered as random with a joint prior distribution (namely a Bingham distribution), which allows the closeness of the two subspaces to be adjusted. Within this framework, the minimum mean-square distance estimator of both subspaces is formulated and implemented via a Gibbs sampler. A simpler scheme based on alternative maximum a posteriori estimation is also presented. The new schemes are shown to provide more accurate estimates of the angles between the subspaces, compared to singular value decomposition based independent estimation of the two subspaces.