We develop a general convergence analysis for a class of inexact Newtontype regularizations for stably solving nonlinear ill-posed problems. Each of the methods under consideration consists of two components: the outer Newton iteration and an inner regularization scheme which, applied to the linearized system, provides the update. In this paper we give a novel and unified convergence analysis w...

Finite-state reactive programs are identiied with nite au-tomata which realize winning strategies in B uchi-Landweber games. The games are speciied by nite \game graphs" equipped with diierent winning conditions (\Rabin condition", \Streett condition" and \Muller con-dition", deened in analogy to the theory of !-automata). We show that for two classes of games with Muller winning condition poly...

Church’s Problem (1957) asks for the construction of a finite-state procedure that transforms any input sequence α letter by letter into an output sequence β such that the pair (α, β) satisfies a given specification. Even after the solution by Büchi and Landweber in 1969 (for specifications in monadic second-order logic over the structure (N,+1)), the problem has stimulated research in automata...

Magnetic tomography is an ill-posed and ill-conditioned inverse problem since, in general, the solution is non-unique and the measured magnetic field is affected by high noise. We use a joint sparsity constraint to regularize the magnetic inverse problem. This leads to a minimization problem whose solution can be approximated by an iterative thresholded Landweber algorithm. The algorithm is pro...

This paper is concerned with the regularization of linear ill-posed problems by a combination of data smoothing and fractional filter methods. For the data smoothing, a wavelet shrinkage denoising is applied to the noisy data with known error level δ. For the reconstruction, an approximation to the solution of the operator equation is computed from the data estimate by fractional filter methods...

This paper is concerned with the numerical solution of an inverse diffraction grating problem, which is to reconstruct a periodic grating profile from measurements of the phaseless diffracted field at a constant height above the grating structure. An efficient continuation method is developed to recover the Fourier coefficients of the periodic grating profile. The continuation proceeds along th...

By augmenting a high resolution full-field Amplitude Modulated Continuous Wave lidar system with a coded aperture, we show that depth-of-field can be extended using explicit, albeit blurred, range data to determine PSF scale. Because complex domain range-images contain explicit range information, the aperture design is unconstrained by the necessity for range determination by depth-from-defocus...

The research presented in this paper addresses the problem of fitting a mathematical model to epidemic data. We propose an implementation of the Landweber iteration to solve locally the arising parameter estimation problem. The epidemic models considered consist of suitable systems of ordinary differential equations. The results presented suggest that the inverse problem approach is a reliable ...

It is well known that iterative algorithms for image deblurring that involve the normal equations show usually a slow convergence. A variant of the normal equations which replaces the conjugate transpose A of the system matrix A with a new matrix is proposed. This approach, which is linked with regularization preconditioning theory and reblurring processes, can be applied to a wide set of itera...