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In this paper we deal with Morozov's discrepancy principle as an a-posteriori parameter choice rule for Tikhonov regularization with general convex penalty terms Ψ for non-linear inverse problems. It is shown that a regularization parameter α fulfilling the discprepancy principle exists, whenever the operator F satisfies some basic conditions, and that for(More)
In this paper, we consider nonlinear inverse problems where the solution is assumed to have a sparse expansion with respect to a preassigned basis or frame. We develop a scheme which allows to minimize a Tikhonov functional where the usual quadratic regu-larization term is replaced by a one–homogeneous (typically weighted p) penalty on the coefficients (or(More)
We shall be concerned with the construction of Tikhonov–based iteration schemes for solving nonlinear operator equations. In particular, we are interested in algorithms for the computation of a minimizer of the Tikhonov functional. To this end, we introduce a replacement functional, that has much better properties than the classical Tikhonov functional with(More)
A level-set based approach for the determination of a piece-wise constant density function from data of its Radon transformat is presented. Simultaneously, a segmentation of the reconstructed density is obtained. The segmenting contour and the corresponding density are found as minimizers of a Mumford-Shah like functional over the set of admissible contours(More)
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(More)
The numerical treatment of systems of partial differential equations (PDEs) is of great interest as many problems from applications belong to that class. Also the optimality system of optimal control problems that is discussed in this work has such a structure. These problems are not elliptic and therefore both the construction of an efficient numerical(More)
We present a fast method for the wavefront reconstruction from pyramid wavefront sensor (P-WFS) measurements. The method is based on an analytical relation between pyramid and Shack-Hartmann sensor (SH-WFS) data. The algorithm consists of two steps--a transformation of the P-WFS data to SH data, followed by the application of cumulative reconstructor with(More)
This paper is devoted to the identification and reconstruction of un-balance distributions in an aircraft engine rotor with a nonlinear damping element. We have developed a rotor model that takes into account the non-linear behavior of a squeeze film damper between the engine's shaft and casing for large oscillation amplitudes. Based on the Tikhonov(More)