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A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data
TLDR
A level-set based approach for the determination of a piecewise constant density function from data of its Radon transform is presented. Expand
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A compressive Landweber iteration for solving ill-posed inverse problems
In this paper we shall be concerned with the construction of an adaptive Landweber iteration for solving linear ill-posed and inverse problems. Classical Landweber iteration schemes provide inExpand
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A Tikhonov-based projection iteration for nonlinear Ill-posed problems with sparsity constraints
TLDR
We develop a scheme which allows to minimize a Tikhonov functional where the usual quadratic regularization term is replaced by a one-homogeneous (typically weighted ℓp) penalty on the coefficients (or isometrically transformed coefficients) of such expansions. Expand
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Regularization by fractional filter methods and data smoothing
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 isExpand
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Convergence analysis of a two-point gradient method for nonlinear ill-posed problems
We perform a convergence analysis of a two-point gradient method which is based on Landweber iteration and on Nesterov's acceleration scheme. Additionally, we show the usefulness of this method viaExpand
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An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
TLDR
We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing $A_n$ compared with standard methods. Expand
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Regularization of ill-posed Mumford-Shah models with perimeter penalization
The problems of existence, stability and convergence of minimizers of a Mumford–Shah functional for the simultaneous reconstruction and segmentation of a distributed parameter in an ill-posedExpand
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MICADO: first light imager for the E-ELT
MICADO will equip the E-ELT with a first light capability for diffraction limited imaging at near-infrared wavelengths. The instrument’s observing modes focus on various flavours of imaging,Expand
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MOROZOV'S DISCREPANCY PRINCIPLE FOR TIKHONOV-REGULARIZATION OF NONLINEAR OPERATORS
ABSTRACT We consider Morozov's discrepancy principle for Tikhonov-regularization of nonlinear operator equations. It is shown that minor restrictions to the operator F and the solution x* of theExpand
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TIGRA—an iterative algorithm for regularizing nonlinear ill-posed problems
We report on a new iterative method for regularizing a nonlinear operator equation in Hilbert spaces. The proposed TIGRA algorithm is a combination of Tikhonov regularization and a gradient methodExpand
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