Ill-posed inverse problems are ubiquitous in applications. Understanding of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering methods have recently been used to solve inverse problems by introducing an artificial dynamical system. This opens up the possibility of using a range of oth...

Initial condition inverse problems are ill-posed and computationally expensive to solve. We present a computational approach for solving inverse problems in the realm of onedimensional contaminant transport. The approach employs finite differencing as a forward solver and probabilistic methods for inversion. Markov Chain Monte Carlo sampling is used to efficiently recover posterior probabilitie...

Regularization is an well-known technique for obtaining stable solution of ill-posed inverse problems. In this paper we establish a key relationship among the regularization methods with an edge-preserving noise filtering method which leads to an efficient adaptive regularization methods. We show experimentally the efficiency and superiority of the proposed regularization methods for some inver...

We address discrete nonlinear inverse problems with weighted least squares and Tikhonov regularization. Regularization is a way to add more information to the problem when it is ill-posed or ill-conditioned. However, it is still an open question as to how to weight this information. The discrepancy principle considers the residual norm to determine the regularization weight or parameter, while ...

Inverse problems involve estimating an underlying continuous function from a set of measurements of some aspect of the function. The mapping from the underlying continuous function to the measurements is known as the forward or direct problem. The forward problem must be a well-posed physical problem. If x is an underlying function and y is a set of measurements, then x and y are related by a f...

Inverse problems are typically ill-posed or ill-conditioned and require regularization. Tikhonov regularization is a popular approach and it requires an additional parameter called the regularization parameter that has to be estimated. The χ method introduced by Mead in [8] uses the χ distribution of the Tikhonov functional for linear inverse problems to estimate the regularization parameter. H...

The rst part of this paper studies a Levenberg-Marquardt scheme for nonlinear inverse problems where the corresponding Lagrange (or regularization) parameter is chosen from an inexact Newton strategy. While the convergence analysis of standard implementations based on trust region strategies always requires the invertibility of the Fr echet derivative of the nonlinear operator at the exact solu...

We address discrete nonlinear inverse problems with weighted least squares and Tikhonov regularization. Regularization is a way to add more information to the problem when it is ill-posed or ill-conditioned. However, it is still an open question as to how to weight this information. The discrepancy principle considers the residual norm to determine the regularization weight or parameter, while ...

the methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. in the geoid computations witho...