In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an order optimal regularization method if the solution is regular in some suitable sense.

A strategy is described for regularizing ill posed structure and nanostructure scattering inverse problems (i.e. structure solution) from complex material structures. This paper describes both the philosophy and strategy of the approach, and a software implementation, DiffPy Complex Modeling Infrastructure (DiffPy-CMI).

The ill-posed problem of determining the shape of a body immersed in a ""at earth" and the mass density within this body from gravity anomaly measurements on the surface of the earth is investigated. Under some a priori assumptions on the structure of the body's boundary a general theorem on uniqueness of the solution is established and some further theorems are derived as immediate consequence...

In this paper we propose an iterative algorithm to solve large size linear inverse ill posed problems. The regularization problem is formulated as a constrained optimization problem. The dual lagrangian problem is iteratively solved to compute an approximate solution. Before starting the iterations, the algorithm computes the necessary smoothing parameters and the error tolerances from the data...

We consider the computation of stable approximations to the exact solution x† of nonlinear ill-posed inverse problems F(x) = y with nonlinear operators F : X → Y between two Hilbert spaces X and Y by the Newton type methods xk+1 = x0 −gαk (

We compare the performance of several robust large-scale minimization algorithms for the unconstrained minimization of an ill-posed inverse problem. The parabolized Navier-Stokes equations model was used for adjoint parameter estimation. The methods compared consist of two versions of the nonlinear conjugate gradient method (CG), Quasi-Newton (BFGS), the limited memory Quasi-Newton (L-BFGS) [15...

Biochemical reaction networks are commonly described by non-linear ODE systems. Model parameters such as rate and equilibrium constants may be unknown or inaccessible and have to be identified from time-series measurements of chemical species. However, parameter identification is an ill-posed inverse problem in the sense that its solution lacks certain stability properties. In particular, model...

We consider the linear inverse problem of reconstructing an unknown finite measure μ from a noisy observation of a generalized moment of μ defined as the integral of a continuous and bounded operator Φ with respect to μ. Motivated by various applications, we focus on the case where the operator Φ is unknown; instead, only an approximation Φm to it is available. An approximate maximum entropy so...

where A is a matrix and x, b are vectors and n is the realization of random noise. We analyze the solution x̂ = A−1b which is completely dominated by noise. A useful solution can only be obtained by using additional information about the true solution x∗. The resulting solution x̂ is called the regularized solution of the inverse problem. Two popular regularization techniques, Tikhonovand total v...

This paper describes a minimax state estimation approach for linear differential-algebraic equations (DAEs) with uncertain parameters. The approach addresses continuous-time DAEs with non-stationary rectangular matrices and uncertain bounded deterministic input. An observation’s noise is supposed to be random with zero mean and unknown bounded correlation function. Main result is a Generalized ...