A new class of disturbance covariance matrix estimators for radar signal processing
applications is introduced following a geometric paradigm. Each estimator is associated with …

The Riemannian geometry of covariance matrices has been essential to several successful
applications, in computer vision, biomedical signal and image processing, and radar data …

Abstract The Barzilai–Borwein (BB) method, an effective gradient descent method with
clever choice of the step length, is adapted from nonlinear optimization to Riemannian …

Algorithms for the computation of the (weighted) geometric mean G of two positive definite
matrices are described and discussed. For large and sparse matrices the problem of …

We propose a new globalization strategy of the damped Newton method for finding
singularities of a vector field on Riemannian manifolds. We establish its global convergence …

When one computes an average of positive definite (PD) matrices, the preservation of
additional matrix structure is desirable for interpretations in applications. An interesting and …

Here we propose a method to classify radar clutter from radar data using an unsupervised
classification algorithm. The data will be represented by Positive Definite Hermitian Toeplitz …

The authors address the estimation of the scatter matrix of a scale mixture of Gaussian
stationary autoregressive (AR) vectors. This is equivalent to consider the estimation of a …

This paper deals with unsupervised radar clutter clustering to characterize pathological
clutter based on their Doppler fluctuations. Operationally, being able to recognize …

Abstract Machine learning models often rely on sparsity, low-rank, orthogonality, correlation,
or graphical structure. The structure of interest in this chapter is geometric, specifically the …