Lipeng Ning

Xianhua Jiang, Lipeng Ning, Tryphon T. Georgiou

We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal prediction. Distances between "infinitesimally close" power spectra are quadratic, and hence, they induce a differential-geometric structure. We study the corresponding Riemannian metrics and, for a particular case, provide explicit formulae for the corresponding geodesics and geodesic distances. The close connection between the geometry of power spectra and the geometry of the Fisher-Rao metric is noted.

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.

Guoping Xu, Jayaram K. Udupa, Jax Luo et al.

Medical image segmentation has advanced rapidly over the past two decades, largely driven by deep learning, which has enabled accurate and efficient delineation of cells, tissues, organs, and pathologies across diverse imaging modalities. This progress raises a fundamental question: to what extent have current models overcome persistent challenges, and what gaps remain? In this work, we provide an in-depth review of medical image segmentation, tracing its progress and key developments over the past decade. We examine core principles, including multiscale analysis, attention mechanisms, and the integration of prior knowledge, across the encoder, bottleneck, skip connections, and decoder components of segmentation networks. Our discussion is organized around seven key dimensions: (1) the shift from supervised to semi-/unsupervised learning, (2) the transition from organ segmentation to lesion-focused tasks, (3) advances in multi-modality integration and domain adaptation, (4) the role of foundation models and transfer learning, (5) the move from deterministic to probabilistic segmentation, (6) the progression from 2D to 3D and 4D segmentation, and (7) the trend from model invocation to segmentation agents. Together, these perspectives provide a holistic overview of the trajectory of deep learning-based medical image segmentation and aim to inspire future innovation. To support ongoing research, we maintain a continually updated repository of relevant literature and open-source resources at https://github.com/apple1986/medicalSegReview

Jun Lyu, Lipeng Ning, William Consagra et al.

High-resolution whole-brain in vivo MR imaging at mesoscale resolutions remains challenging due to long scan durations, motion artifacts, and limited signal-to-noise ratio (SNR). This study proposes Rotating-view super-resolution (ROVER)-MRI, an unsupervised framework based on multi-scale implicit neural representations (INR), enabling efficient recovery of fine anatomical details from multi-view thick-slice acquisitions. ROVER-MRI employs coordinate-based neural networks to implicitly and continuously encode image structures at multiple spatial scales, simultaneously modeling anatomical continuity and correcting inter-view motion through an integrated registration mechanism. Validation on ex-vivo monkey brain data and multiple in-vivo human datasets demonstrates substantially improved reconstruction performance compared to bicubic interpolation and state-of-the-art regularized least-squares super-resolution reconstruction (LS-SRR) with 2-fold reduction in scan time. Notably, ROVER-MRI achieves an unprecedented whole-brain in-vivo T2-weighted imaging at 180 micron isotropic resolution in only 17 minutes of scan time on a 7T scanner with 22.4% lower relative error compared to LS-SRR. We also demonstrate improved SNR using ROVER-MRI compared to a time-matched 3D GRE acquisition. Quantitative results on several datasets demonstrate better sharpness of the reconstructed images with ROVER-MRI for different super-resolution factors (5 to 11). These findings highlight ROVER-MRI's potential as a rapid, accurate, and motion-resilient mesoscale imaging solution, promising substantial advantages for neuroimaging studies.