Related papers: A Tikhonov Regularization Based Algorithm for Scat…

In ground based infrared imaging a well-known technique to reduce the influence of thermal and background noise is chopping and nodding, where four different signals of the same object are recorded from which the object is reconstructed…

It is a well-known fact that adding noise to the input data often improves network performance. While the dropout technique may be a cause of memory loss, when it is applied to recurrent connections, Tikhonov regularization, which can be…

We propose an efficient and flexible method for solving Abel integral equation of the first kind, frequently appearing in many fields of astrophysics, physics, chemistry, and applied sciences. This equation represents an ill-posed problem,…

This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…

In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…

This paper presents an error analysis of classical and learned Tikhonov regularization schemes for inverse problems. We first demonstrate, both theoretically and numerically, that using a fixed regularization parameter across varying noise…

We study inverse problems F(f) = g with perturbed right hand side g^{obs} corrupted by so-called impulsive noise, i.e. noise which is concentrated on a small subset of the domain of definition of g. It is well known that Tikhonov-type…

All signals obtained as instrumental response of analytical apparatus are affected by noise, as in Raman spectroscopy. Whereas Raman scattering is an inherently weak process, the noise background can lead to misinterpretations. Although…

We consider the signal reconstruction problem under the case of the signals sampled in the multichannel way and with the presence of noise. Observing that if the samples are inexact, the rigorous enforcement of multichannel interpolation is…

A numerical scheme that uses multi-frequency Newton iterations to reconstruct a rough surface profile between two dielectric media is proposed. At each frequency sample, the scheme employs Newton iterations to solve the nonlinear inverse…

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…

In this work, we consider ill-posed inverse problems in which the forward operator is continuous and weakly closed, and the sought solution belongs to a weakly closed constraint set. We propose a regularization method based on minimizing…

In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…

We study weighted Tikhonov regularization for large-scale linear discrete ill-posed problems with random noise. Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, we derive stochastic…

In this paper, we investigate regularization of linear inverse problems with irregular noise. In particular, we consider the case that the noise can be preprocessed by certain adjoint embedding operators. By introducing the consequent…

We present an extension of the linear sampling method for solving the sound-soft inverse scattering problem in two dimensions with data generated by randomly distributed small scatterers. The theoretical justification of our novel sampling…

This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy…

We consider the problem of reconstructing the shape of an impenetrable sound-soft obstacle from scattering measurements. The input data is assumed to be the far-field pattern generated when a plane wave impinges on an unknown obstacle from…

In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…

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…