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Reconstructing and tracking dynamic 3D scenes remains a fundamental challenge in computer vision. Existing approaches often decouple geometry from motion: multi-view reconstruction methods assume static scenes, while dynamic tracking…
We propose a weighted least-square (WLS) method to design autoregressive moving average (ARMA) graph filters. We first express the WLS design problem as a numerically-stable optimization problem using Chebyshev polynomial bases. We then…
Purpose: In multi-spectral imaging (MSI), several fast spin echo volumes with discrete Larmor frequency offsets are acquired in an interleaved fashion with multiple concatenations. Here, a variable resolution (VR) method to nearly halve…
This paper introduces two novel approaches for Online Multi-Task Learning (MTL) Regression Problems. We employ a high performance graph-based MTL formulation and develop two alternative recursive versions based on the Weighted Recursive…
Physics-Informed Neural Networks (PINNs) show significant potential for solving inverse problems, especially when observations are limited and sparse, provided that the relevant physical equations are known. We use PINNs to estimate smooth…
This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard l1 -minimization algorithm, originally proposed in the context…
We report a new workflow for background-oriented schlieren (BOS), termed "physics-informed BOS," to extract density, velocity, and pressure fields from a pair of reference and distorted images. Our method uses a physics-informed neural…
Purpose: To develop and evaluate a free-breathing respiratory motion compensated 4D (3D+respiration) $T_2$-weighted turbo spin echo sequence with application to radiology and MR-guided radiotherapy. Methods: k-space data are continuously…
This paper introduces wavelet-physics-informed residual neural networks (W-PIRNNs) to study complex fluid flow problems by reconstructing the flow field from highly sparse, supervised data. Our W-PIRNNs fundamentally integrate ResNet and…
This study presents an unsupervised, motion-resolved reconstruction framework for high-resolution, free-breathing pulmonary magnetic resonance imaging (MRI), utilizing a three-dimensional Gaussian representation (3DGS). The proposed method…
Solving the global method of Weighted Least Squares (WLS) model in image filtering is both time- and memory-consuming. In this paper, we present an alternative approximation in a time- and memory- efficient manner which is denoted as…
Altered hemodynamics play a key role in cerebrovascular diseases such as aneurysms and stenosis. However, in vivo imaging lacks the spatial resolution required to resolve flow dynamics in small vessels. This study presents an experimental…
We propose a new least squares finite element method to solve the Poisson equation. By using a piecewisely irrotational space to approximate the flux, we split the classical method into two sequential steps. The first step gives the…
The novel neural networks show great potential in solving partial differential equations. For single-phase flow problems in subsurface porous media with high-contrast coefficients, the key is to develop neural operators with accurate…
We propose a data-driven algorithm for reconstructing the irregular, chaotic flow dynamics around two side-by-side square cylinders from sparse, time-resolved, velocity measurements in the wake. We use Proper Orthogonal Decomposition (POD)…
Accurate three-dimensional (3D) reconstruction of cardiac chamber motion from time-resolved medical imaging modalities is of growing interest in both the clinical and biomechanical fields. Despite recent advancement, the cardiac motion…
Least-squares reverse time migration (LSRTM) is one of the classic seismic imaging methods to reconstruct model perturbations within a known reference medium. It can be computed in either data or image domain using different methods by…
This paper presents novel adaptive space-time reduced-rank interference suppression least squares algorithms based on joint iterative optimization of parameter vectors. The proposed space-time reduced-rank scheme consists of a joint…
We address the problem of recovering a time-varying 4D distribution from a sparse sequence of 2D projections - analogous to novel-view synthesis from sparse cameras, but applied to the 4D transverse phase space density $\rho(x,p_x,y,p_y)$…
Reconstructing scalar fields from error-embedded gradient measurements is a fundamental linear inverse problem with broad applications in computational physics. Conventional approaches, such as Poisson-based solvers and the Green's Function…