Towards a median signal detector through the total Bregman divergence and its robustness analysis

A novel family of geometric signal detectors are proposed through medians of the total Bregman diver-gence (TBD), which are shown advantageous over the conventional methods and their mean counterparts. By interpreting the observation data as Hermitian positive-definite matrices, their mean or median play an essential role in signal detection. As is difficult to be solved analytically, we propose numerical solu-tions through Riemannian gradient descent algorithms or fixed-point algorithms.Beside detection performance, robustness of a detector to outliers is also of vital importance, which can often be analyzed via the influence functions. Introducing an orthogonal basis for Hermitian matrices, we are able to compute the corresponding influence functions analytically and exactly by solving a linear system, which is transformed from the governing matrix equation. Numerical simulations show that the TBD medians are more robust than their mean counterparts.(c) 2022 Elsevier B.V. All rights reserved.