William Consagra

Mohammed Munzer Dwedari, William Consagra, Philip Müller et al.

The Orientation Distribution Function (ODF) characterizes key brain microstructural properties and plays an important role in understanding brain structural connectivity. Recent works introduced Implicit Neural Representation (INR) based approaches to form a spatially aware continuous estimate of the ODF field and demonstrated promising results in key tasks of interest when compared to conventional discrete approaches. However, traditional INR methods face difficulties when scaling to large-scale images, such as modern ultra-high-resolution MRI scans, posing challenges in learning fine structures as well as inefficiencies in training and inference speed. In this work, we propose HashEnc, a grid-hash-encoding-based estimation of the ODF field and demonstrate its effectiveness in retaining structural and textural features. We show that HashEnc achieves a 10% enhancement in image quality while requiring 3x less computational resources than current methods. Our code can be found at https://github.com/MunzerDw/NODF-HashEnc.

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.

William Consagra, Zhiling Gu, Zhengwu Zhang

We propose a novel deep neural network methodology for density estimation on product Riemannian manifold domains. In our approach, the network directly parameterizes the unknown density function and is trained using a penalized maximum likelihood framework, with a penalty term formed using manifold differential operators. The network architecture and estimation algorithm are carefully designed to handle the challenges of high-dimensional product manifold domains, effectively mitigating the curse of dimensionality that limits traditional kernel and basis expansion estimators, as well as overcoming the convergence issues encountered by non-specialized neural network methods. Extensive simulations and a real-world application to brain structural connectivity data highlight the clear advantages of our method over the competing alternatives.

William Consagra, Arun Venkataraman, Xing Qiu

Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the traditional techniques from functional data analysis are plagued by the curse of dimensionality and quickly become intractable as the dimension of the domain increases. In this paper, we propose a framework for learning continuous representations from a sample of multidimensional functional data that is immune to several manifestations of the curse. These representations are constructed using a set of separable basis functions that are defined to be optimally adapted to the data. We show that the resulting estimation problem can be solved efficiently by the tensor decomposition of a carefully defined reduction transformation of the observed data. Roughness-based regularization is incorporated using a class of differential operator-based penalties. Relevant theoretical properties are also established. The advantages of our method over competing methods are demonstrated in a simulation study. We conclude with a real data application in neuroimaging.