Related papers: New-generation Maximum Entropy Method (ngMEM): a L…
In the field of fluid numerical analysis, there has been a long-standing problem: lacking of a rigorous mathematical tool to map from a continuous flow field to discrete vortex particles, hurdling the Lagrangian particles from inheriting…
The Expectation--Maximization (EM) algorithm is a simple meta-algorithm that has been used for many years as a methodology for statistical inference when there are missing measurements in the observed data or when the data is composed of…
We propose a new approach for the accurate reconstruction of cosmic microwave background distributions from observations containing in addition to the primary fluctuations the radiation from unresolved extragalactic point sources and pixel…
Horizon-scale imaging with the Event Horizon Telescope (EHT) has provided transformative insights into supermassive black holes but its resolution and scope are limited by ground-based constraints such as the size of the Earth, its…
Super-resolution fluorescence microscopy, with a resolution beyond the diffraction limit of light, has become an indispensable tool to directly visualize biological structures in living cells at a nanometer-scale resolution. Despite…
Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…
Accurate null depth retrieval is critical in nulling interferometry. However, achieving accurate null depth calibration is challenging due to various noise sources, instrumental imperfections, and the complexity of real observational…
Diffeomorphic registration using optimal control on the diffeomorphism group and on shape spaces has become widely used since the development of the Large Deformation Diffeomorphic Metric Mapping (LDDMM) algorithm. More recently, a series…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
An inverse iterative algorithm for microwave imaging based on moment method solution is presented here. The iterative scheme has been developed on constrained optimization technique and is certain to converge. Different mesh size for the…
Nonlinear Mixed Effects models (NLME) models are widely used in pharmacometrics and related fields to analyze hierarchical and longitudinal data. However, as the number of parameters and random effects increases, traditional methods for…
Reconstructing an image from sparsely sampled Fourier data is an ill-posed inverse problem that occurs in a variety of subjects within science, including the data analysis for Very Long Baseline Interferometry (VLBI) and the…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
With the advent of infrared long-baseline interferometers with more than two telescopes, both the size and the completeness of interferometric data sets have significantly increased, allowing images based on models with no a priori…
This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. MESP has been widely applied to many areas, including…
Very-long-baseline interferometry (VLBI) at frequencies above 230 GHz with Earth-diameter baselines gives spatial resolution finer than the ${\sim}50 \mu$as "shadow" of the supermassive black hole at the Galactic Center, Sagittarius A* (Sgr…
The rapid expansion of electric vehicles has intensified the need for accurate and efficient diagnosis of lithium-ion batteries. Parameter identification of electrochemical battery models is widely recognized as a powerful method for…
In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…
The sparse interferometric coverage of the Event Horizon Telescope (EHT) poses a significant challenge for both reconstruction and model fitting of black-hole images. PRIMO is a new principal components analysis-based algorithm for image…
We introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when…