This paper surveys an important class of methods that combine iterative projection methods
and variational regularization methods for large-scale inverse problems. Iterative methods …

Acoustic tomography is a technique widely used in nonintrusive temperature measurement.
The time of flight (TOF) of acoustic waves can be used to estimate the temperatures of a …

Image segmentation is of great importance in image processing. In this paper, we propose a
two-stage image segmentation strategy based on the nonconvex ℓ 2− ℓ p approximation of …

Ill-posed problems arise in many areas of science and engineering. Their solutions, if they
exist, are very sensitive to perturbations in the data. Regularization aims to reduce this …

The need to solve discrete ill-posed problems arises in many areas of science and
engineering. Solutions of these problems, if they exist, are very sensitive to perturbations in …

In this paper we develop flexible Krylov methods for efficiently computing regularized
solutions to large-scale linear inverse problems with an \ell_2 fit-to-data term and an \ell_p …

Discrete ill-posed inverse problems arise in various areas of science and engineering. The
presence of noise in the data often makes it difficult to compute an accurate approximate …

Inference by means of mathematical modeling from a collection of observations remains a
crucial tool for scientific discovery and is ubiquitous in application areas such as signal …

Image reconstruction problems, like image deblurring and computer tomography, are
usually ill-posed and require regularization. A popular approach to regularization is to …

In this paper, we focus on the numerical solution of nonlinear inverse problems in applied
geophysics. Our aim is to reconstruct the structure of the soil, ie, either its electrical …