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The random demodulator is a recent compressive sensing architecture providing efficient sub-Nyquist sampling of sparse band-limited signals. The compressive sensing paradigm requires an accurate model of the analog front-end to enable…
A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…
Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods,…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
We propose a novel mesh refinement scheme based on signal processing for boundary integral simulations of inviscid droplet dynamics with axial symmetry. A key idea is to directly access the Fourier coefficients of a principal curvature as a…
Continual fine-tuning aims to adapt a pre-trained backbone to new tasks sequentially while preserving performance on earlier tasks whose data are no longer available. Existing approaches fall into two categories which include input- and…
This study assesses a Continuous Data Assimilation (CDA) dynamical-downscaling algorithm for enhancing the simulation of the Indian summer monsoon (ISM) system. CDA is a mathematically rigorous technique that has been recently introduced to…
Spatial resolution of depth sensors is often significantly lower compared to that of conventional optical cameras. Recent work has explored the idea of improving the resolution of depth using higher resolution intensity as a side…
In this paper we introduce and analyze an algorithm for continuous data assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model of porous media. This model is believed to be accurate when the flow velocity…
This paper proposes a novel algorithm for signal classification problems. We consider a non-stationary random signal, where samples can be classified into several different classes, and samples in each class are identically independently…
Direct ptychography enables the retrieval of information encoded in the phase of an electron wave passing through a thin sample by deconvolving the interference effects of a converged probe with known aberrations. Under the weak phase…
We study a continuous data assimilation (CDA) algorithm for a velocity-vorticity formulation of the 2D Navier-Stokes equations in two cases: nudging applied to the velocity and vorticity, and nudging applied to the velocity only. We prove…
Differentially private (DP) mechanisms face the challenge of providing accurate results while protecting their inputs: the privacy-utility trade-off. A simple but powerful technique for DP adds noise to sensitivity-bounded query outputs to…
The purpose of this study is to provide a new methodology of how one can consistently estimate a change-point in time series data. In contrast with previous studies, the suggested methodology employs only the empirical spectral density and…
Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a…
Encoding a sequence of observations is an essential task with many applications. The encoding can become highly efficient when the observations are generated by a dynamical system. A dynamical system imposes regularities on the observations…
An accurate treatment of electronic spectra in large systems with a technique such as time dependent density functional theory (TDDFT) is computationally challenging. Due to the Nyquist sampling theorem, direct real time simulations must be…