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Cosmic microwave background radiation (CMB) is critical to the understanding of the early universe and precise estimation of cosmological constants. Due to the contamination of thermal dust noise in the galaxy, the CMB map that is an image…
Magnetic resonance imaging (MRI) offers the flexibility to image a given anatomic volume under a multitude of tissue contrasts. Yet, scan time considerations put stringent limits on the quality and diversity of MRI data. The gold-standard…
Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models,…
A new maximum likelihood estimation approach for blind channel equalization, using variational autoencoders (VAEs), is introduced. Significant and consistent improvements in the error rate of the reconstructed symbols, compared to constant…
Evaluation in scientific reconstruction is dominated by pointwise metrics - RMSE, MAE, per-event resolution - under the implicit assumption that lower error means better reconstruction. We show that this assumption fails structurally for…
Travel-time tomography forces a trade-off between mesh resolution and stability in which the regularizer choice dominates what can be recovered. We introduce MIMIR, a differentiable framework that represents the 2D velocity field as a…
Purpose: To develop a unified image reconstruction framework that bridges real-time and gated cardiac MRI, including quantitative MRI. Methods: We introduce Generative Multitasking, which learns an implicit neural temporal basis from…
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…
The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…
Gaussian process regression has recently emerged as a powerful, system-agnostic tool for building global potential energy surfaces (PES) of polyatomic molecules. While the accuracy of GP models of PES increases with the number of potential…
A virtual element method (VEM) with the first order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background…
The wavelet Maximum Entropy on the Mean (wMEM) approach to the MEG inverse problem is revisited and extended to infer brain activity from full space-time data. The resulting dimensionality increase is tackled using a collection of…
This article considers the inverse problem of Magnet resonance electrical impedance tomography (MREIT) in two dimensions. A rigorous mathematical framework for this inverse problem as well as the existing Harmonic $B_z$ Algorithm as a…
We recently published an approach named ROVir (Region-Optimized Virtual coils) that uses the beamforming capabilities of a multichannel magnetic resonance imaging (MRI) receiver array to achieve coil compression (reducing an original set of…
Low-light enhancement has wide applications in autonomous driving, 3D reconstruction, remote sensing, surveillance, and so on, which can significantly improve information utilization. However, most existing methods lack generalization and…
The kernel reconstruction is a method that reduces noise in dynamic positron emission tomography (PET) by exploiting spatial correlations in the PET image. Although this method works well for large anatomical regions with relatively slow…
Incommensurate heterostructures of two-dimensional (2D) materials, despite their attractive electronic behaviour, are challenging to simulate because of the absence of translation symmetry. Experimental investigations of these structures…
In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], allows solving multiscale parameter-dependent problems at a…
In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with $\ell_1$-loss, where the goal is to recover a low-rank matrix from a limited number of…