Related papers: Convergence rates for inverse Problems in Hilbert …
The convergence rates results in $\ell^1$-regularization when the sparsity assumption is narrowly missed, presented by Burger et al. (2013 Inverse Problems 29 025013), are based on a crucial condition which requires that all basis elements…
In the literature on singular perturbation (Lavrentiev regularization) for the stable approximate solution of operator equations with monotone operators in the Hilbert space the phenomena of conditional stability and local well-posedness…
Regularization plays a pivotal role in ill-posed machine learning and inverse problems. However, the fundamental comparative analysis of various regularization norms remains open. We establish a small noise analysis framework to assess the…
The authors study Tikhonov regularization of linear ill-posed problems with a general convex penalty defined on a Banach space. It is well known that the error analysis requires smoothness assumptions. Here such assumptions are given in…
We investigate a level-set type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable…
This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…
In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very…
We study the recovery of a spatially dependent source in a one-dimensional space-time fractional wave equation using boundary measurement data collected at a single endpoint. The main challenge arises from the fact that the eigenfunctions…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
A Tikhonov regularized inertial primal\mbox{-}dual dynamical system with time scaling and vanishing damping is proposed for solving a linearly constrained convex optimization problem in Hilbert spaces. The system under consideration…
We investigate Tikhonov regularization methods for nonlinear ill-posed problems in Banach spaces, where the penalty term is described by Bregman distances. We prove convergence and stability results. Moreover, using appropriate source…
Many inverse problems are concerned with the estimation of non-negative parameter functions. In this paper, in order to obtain non-negative stable approximate solutions to ill-posed linear operator equations in a Hilbert space setting, we…
We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions…
Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method…
We consider joint Tikhonov- and Lavrentiev-regularization of control problems with pointwise control- and state-constraints. We derive error estimates for the error which is introduced by the Tikhonov regularization. With the help of this…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
In this paper we provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called method of quasi solutions) with some versions of the discrepancy…
In this paper we utilise new methods of Calculus of Variations in $L^\infty$ to provide a regularisation strategy to the ill-posed inverse problem of identifying the source of a non-homogeneous linear elliptic equation, satisfying Dirichlet…
So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…