Related papers: Numerical methods for parameter identification in …
In this paper, we investigate the state estimation problem over multiple Markovian packet drop channels. In this problem setup, a remote estimator receives measurement data transmitted from multiple sensors over individual channels. By the…
Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative…
We present DARTR: a Data Adaptive RKHS Tikhonov Regularization method for the linear inverse problem of nonparametric learning of function parameters in operators. A key ingredient is a system intrinsic data-adaptive (SIDA) RKHS, whose norm…
We consider the stable approximation of sparse solutions to non-linear operator equations by means of Tikhonov regularization with a subquadratic penalty term. Imposing certain assumptions, which for a linear operator are equivalent to the…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the…
Sparsity of a learning solution is a desirable feature in machine learning. Certain reproducing kernel Banach spaces (RKBSs) are appropriate hypothesis spaces for sparse learning methods. The goal of this paper is to understand what kind of…
We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…
This paper investigates the convergence rate for Tikhonov regularization of the problem of identifying the coefficient $a \in L^{\infty}(\Omega)$ in the Robin-boundary equation $-\mathrm{div}(a\nabla u)-bu=f,~ x \in \Omega \subset \mathbb…
We consider linear inverse problems that are formulated in the continuous domain. The object of recovery is a function that is assumed to minimize a convex objective functional. The solutions are constrained by imposing a continuous-domain…
This article presents a mathematical study of the problem of identifying a time-dependent source term in transport processes described by a timefractional parabolic equation, based on noisy time-dependent measurements taken at an arbitrary…
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…
Understanding the orientation of geological structures is crucial for analyzing the complexity of the Earths' subsurface. For instance, information about geological structure orientation can be incorporated into local anisotropic…
The feasibility of uniquely estimating parameters of dynamical systems from observations is a widely discussed aspect of mathematical modelling. Several approaches have been published for analyzing identifiability. However, they are…
Non-stationary blind super-resolution is an extension of the traditional super-resolution problem, which deals with the problem of recovering fine details from coarse measurements. The non-stationary blind super-resolution problem appears…
In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
This paper studies Tikhonov regularization for finitely smoothing operators in Banach spaces when the penalization enforces too much smoothness in the sense that the penalty term is not finite at the true solution. In a Hilbert space…