Related papers: Regularization operators for identifying the unkno…
In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
We recently developed a new approach to get a stabilized image from a sequence of frames acquired through atmospheric turbulence. The goal of this algorihtm is to remove the geometric distortions due by the atmosphere movements. This method…
A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as…
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation measured on an arc of the boundary, we propose a numerical…
The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the…
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
In this paper, modulating functions-based method is proposed for estimating space-time dependent unknowns in one-dimensional partial differential equations. The proposed method simplified the problem into a system of algebraic equations…
We present a method for finding optimal controllers for unknown, time-varying, dynamic systems which can be re-initialized from a given initial condition repeatedly, in which the performance measure is available for sampling with noise, but…
This paper investigates the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location:…
This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data $u(x_0,t,\omega).$ We build the…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
In this work, forward and inverse problems for a time-fractional pseudo-parabolic equation $D_t^{\rho} [u(t) + \mu Au(t)] + \sigma(t) Au(t) = r(t)g$ are investigated in a Hilbert space, where $A$ is an unbounded, positive, self-adjoint…
Time series forecasting typically needs to address non-stationary data with evolving trend and seasonal patterns. To address the non-stationarity, reversible instance normalization has been recently proposed to alleviate impacts from the…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…
We consider the inverse source problem of determining a source term depending on both time and space variable for fractional and classical diffusion equations in a cylindrical domain from boundary measurements. With suitable boundary…
Tikhonov regularization is one of the most commonly used methods of regularization of ill-posed problems. In the setting of finite element solutions of elliptic partial differential control problems, Tikhonov regularization amounts to…
Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect…
We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of…