Environment measurement is an important issue for various applications including household robots. Pulse radars are promising candidates in a near future. Estimating target shapes using waveform data, which we obtain by scanning an omni-directional antenna, is known as one of ill-posed inverse problems. Parametric methods such as Model-fitting method have problems concerning calculation time an...

Since the classical iterative methods for solving nonlinear ill-posed problems are locally convergent, this paper constructs a robust and widely convergent method for identifying parameter based on homotopy algorithm, and investigates this method’s convergence in the light of Lyapunov theory. Furthermore, we consider 1-D elliptic type equation to testify that the homotopy regularization can ide...

Following a discussion of the relation of these problems to applications , intended to clarify the considerations which must be handled in order to obtain genuinely useful results, we consider techniques for determining optimal approximationss and consequent optimal error bounds for certain classes of ill-posed problems with appropriate a priori information.

Whenever one is confronted with the necessity to measure some quantities, which are not accessible directly, however, are linked via a mathematical model to some measurement data, one has to solve an inverse problem. In this context we speak of a direct problem, when expected measurement data are calculated from a mathematical model, when the not directly accessible quantities are given and, on...

In this paper we consider the iteratively regularized Gauss–Newton method for solving nonlinear ill-posed inverse problems. Under merely the 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.

In this paper we study some properties of the classical Arnoldi based methods for solving infinite dimensional linear equations involving compact operators. These problems are intrinsically ill-posed since a compact operator does not admit a bounded inverse. We study the convergence properties and the ability of these algorithms to estimate the dominant singular values of the operator.

We consider a regularized Levenberg–Marquardt method for solving nonlinear ill-posed inverse problems. We use the discrepancy principle to terminate the iteration. Under certain conditions, we prove the convergence of the method and obtain the order optimal convergence rates when the exact solution satisfies suitable source-wise representations. Mathematics Subject Classification (2000) 65J15 ·...

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 study global optimization (GOP) in the framework of non-linear inverse problems with a unique solution. These problems are in general ill-posed. Evaluation of the objective function is often expensive, as it implies the solution of a non-trivial forward problem. The ill-posedness of these problems calls for regularization while the high evaluation cost of the objective function can be addres...