Related papers: Iterative algorithms for a non-linear inverse prob…
The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control. To this end, this work presents a learning-based…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
We look at continuum solutions in optimisation problems associated to linear inverse problems $y = Ax$ with non-negativity constraint $x \geq 0$. We focus on the case where the noise model leads to maximum likelihood estimation through…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
We consider a least absolute deviation (LAD) approach to the robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise. To solve the resulting non-convex optimization problem, we…
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the…
Iterative deblurring, notably the Richardson-Lucy algorithm with and without regularization, is analyzed in the context of nuclear and high-energy physics applications. In these applications, probability distributions may be discretized…
We consider an inverse problem of recovering a potential associated to a semi-linear wave equation with a quadratic nonlinearity in $1 + 1$ dimensions. We develop a numerical scheme to determine the potential from a noisy…
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based…
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise…
Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…
We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…
We present a non-iterative algorithm to reconstruct the isotropic acoustic wave speed from the measurement of the Neumann-to-Dirichlet map. The algorithm is designed based on the boundary control method and involves only computations that…
We present an algorithm based on numerical techniques that have become standard for solving nonlinear integral equations: Newton's method, homotopy continuation, the multilevel method and random projection to solve the inversion problem…
We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…