相关论文: Robust and tractable multidimensional exponential …
Numerous signals in relevant signal processing applications can be modeled as a sum of complex exponentials. Each exponential term entails a particular property of the modeled physical system, and it is possible to define families of…
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…
The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…
In this paper, we show that sparse signals f representable as a linear combination of a finite number N of spikes at arbitrary real locations or as a finite linear combination of B-splines of order m with arbitrary real knots can be almost…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
We present the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm, recently proposed in [Li and Hu, {\it J. Comput. Phys.}, 2021], for efficiently solving subdiffusion equations with heterogeneous coefficients in long time. This…
We consider the problem of reconstructing a sparse signal $x^0\in\R^n$ from a limited number of linear measurements. Given $m$ randomly selected samples of $U x^0$, where $U$ is an orthonormal matrix, we show that $\ell_1$ minimization…
We consider the problem of estimating high-dimensional covariance matrices of $K$-populations or classes in the setting where the sample sizes are comparable to the data dimension. We propose estimating each class covariance matrix as a…
For an arbitrary parameter $p\in [1,+\infty]$, we consider the problem of exponential stabilization in the spatial $L^{p}$-norm, and $W^{1,p}$-norm, respectively, for a class of anti-stable linear parabolic PDEs with space-time-varying…
In this paper we introduce a new sampling and reconstruction approach for multi-dimensional analog signals. Building on top of the Unlimited Sensing Framework (USF), we present a new folded sampling operator called the multi-dimensional…
In the process of reproducing the state dynamics of parameter dependent distributed systems, data from physical measurements can be incorporated into the mathematical model to reduce the parameter uncertainty and, consequently, improve the…
We consider the multivariate max-linear regression problem where the model parameters $\boldsymbol{\beta}_{1},\dotsc,\boldsymbol{\beta}_{k}\in\mathbb{R}^{p}$ need to be estimated from $n$ independent samples of the (noisy) observations $y =…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
We study the recovery of sparse signals from underdetermined linear measurements when a potentially erroneous support estimate is available. Our results are twofold. First, we derive necessary and sufficient conditions for signal recovery…
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…
Optimization-based problems have become of great interest for signal approximation purposes, as they achieved good accuracy results while being extremely flexible and versatile. In this work, we put our focus on the context of periodic…
The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been…
Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…
In this article, we construct empirical likelihood (EL)-weighted estimators of linear functionals of a probability measure in the presence of side information. Motivated by nuisance parameters in semiparametric models with possibly infinite…