Lipeng Ning

Lipeng Ning, Tryphon T. Georgiou

It is perhaps not widely recognized that certain common notions of distance between probability measures have an alternative dual interpretation which compares corresponding functionals against suitable families of test functions. This dual viewpoint extends in a straightforward manner to suggest metrics between matrix-valued measures. Our main interest has been in developing weakly-continuous metrics that are suitable for comparing matrix-valued power spectral density functions. To this end, and following the suggested recipe of utilizing suitable families of test functions, we develop a weakly-continuous metric that is analogous to the Wasserstein metric and applies to matrix-valued densities. We use a numerical example to compare this metric to certain standard alternatives including a different version of a matricial Wasserstein metric developed earlier.

Lipeng Ning, Xianhua Jiang, Tryphon Georgiou

We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and compare several alternatives metrics and divergence measures. We advocate a specific one which represents the Wasserstein distance between the corresponding Gaussians distributions and show that it coincides with the so-called Bures/Hellinger distance between covariance matrices as well. Most importantly, besides the physically appealing interpretation, computation of the metric requires solving a linear matrix inequality (LMI). As a consequence, computations scale nicely for problems involving large covariance matrices, and linear prior constraints on the covariance structure are easy to handle. We compare this transportation/Bures/Hellinger metric with the maximum likelihood and the Burg methods as to their performance with regard to estimation of power spectra with spectral lines on a representative case study from the literature.

Chenjun Li, Dian Yang, Shun Yao et al.

In this study, we developed an Evidence-based Ensemble Neural Network, namely EVENet, for anatomical brain parcellation using diffusion MRI. The key innovation of EVENet is the design of an evidential deep learning framework to quantify predictive uncertainty at each voxel during a single inference. To do so, we design an evidence-based ensemble learning framework for uncertainty-aware parcellation to leverage the multiple dMRI parameters derived from diffusion MRI. Using EVENet, we obtained accurate parcellation and uncertainty estimates across different datasets from healthy and clinical populations and with different imaging acquisitions. The overall network includes five parallel subnetworks, where each is dedicated to learning the FreeSurfer parcellation for a certain diffusion MRI parameter. An evidence-based ensemble methodology is then proposed to fuse the individual outputs. We perform experimental evaluations on large-scale datasets from multiple imaging sources, including high-quality diffusion MRI data from healthy adults and clinically diffusion MRI data from participants with various brain diseases (schizophrenia, bipolar disorder, attention-deficit/hyperactivity disorder, Parkinson's disease, cerebral small vessel disease, and neurosurgical patients with brain tumors). Compared to several state-of-the-art methods, our experimental results demonstrate highly improved parcellation accuracy across the multiple testing datasets despite the differences in dMRI acquisition protocols and health conditions. Furthermore, thanks to the uncertainty estimation, our EVENet approach demonstrates a good ability to detect abnormal brain regions in patients with lesions, enhancing the interpretability and reliability of the segmentation results.