Related papers: Shape and parameter identification by the linear s…
The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
In this study, we develop a continuous data assimilation algorithm to recover the parameter $\alpha$ in the simplified Bardina model. Our method utilizes the observations of finitely many Fourier modes by using a nudging framework that…
The shape of liquid droplets in air plays an important role in aerodynamic behavior and combustion dynamics of miniaturized propulsion systems such as microsatellites and small drones. Their precise manipulation can yield optimal efficiency…
In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Consider the inverse random source scattering problem for the two-dimensional time-harmonic elastic wave equation with an inhomogeneous, anisotropic mass density. The source is modeled as a microlocally isotropic generalized Gaussian random…
In this work, we consider the problem of reconstructing the shape of a three dimensional impenetrable sound-soft axis-symmetric obstacle from measurements of the scattered field at multiple frequencies. This problem has important…
Solving an ill-posed linear inverse problem requires knowledge about the underlying signal model. In many applications, this model is a priori unknown and has to be learned from data. However, it is impossible to learn the model using…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…
A new statistical procedure, based on a modified spline basis, is proposed to identify the linear components in the panel data model with fixed effects. Under some mild assumptions, the proposed procedure is shown to consistently estimate…
We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…
We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…
The primary objective of this research is to investigate an inverse problem of parameter identification in nonlinear mixed quasi-variational inequalities posed in a Banach space setting. By using a fixed point theorem, we explore properties…
In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it's dual space. The Factorization Method uses Picard's Criteria to define an indicator function to…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…