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- Ronny Ramlau, Wolfgang Ring
- J. Comput. Physics
- 2007

Abstract. A level-set based approach for the determination of a piecewise 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… (More)

In this paper we deal with Morozov’s discrepancy principle as an aposteriori 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)

Abstract. In this paper, we investigate the regularization properties of Tikhonov regularization with a sparsity (or Besov) penalty for the inversion of nonlinear operator equations. We propose an a posteriori parameter choice rule that ensures convergence in the used norm as the data error goes to zero. We show that the method of surrogate functionals will… (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)

This paper presents a level-set based approach for the simultaneous reconstruction and segmentation of the activity as well as the density distribution from tomography data gathered by an integrated SPECT/CT scanner. Activity and density distributions are modelled as piecewise constant functions. The segmenting contours and the corresponding function values… (More)

- Ronny Ramlau, Gerd Teschke
- Numerische Mathematik
- 2006

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 regularization term is replaced by a one–homogeneous (typically weighted `p) penalty on the coefficients (or… (More)

- Ronny Ramlau, Gerd Teschke
- 2005

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)

- Gerd Teschke, Ronny Ramlau
- 2007

This paper is concerned with nonlinear inverse problems where data and solution are vector valued and, moreover, where the solution is assumed to have a sparse expansion with respect to a preassigned frame. We especially focus on such problems where the different components of the solution exhibit a common or so–called joint sparsity pattern. Joint sparsity… (More)

- Ronny Ramlau
- 2008

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 in combination with suitable regularization parameter rules order optimal regularization schemes. However, for many applications the implementation of Landweber’s method… (More)

- Peter Maass, Sergei V. Pereverzyev, Ronny Ramlau, Sergei G. Solodky
- Numerische Mathematik
- 2001

The aim of this paper is to describe an eecient adaptive strategy for discretizing ill-posed linear operator equations of the rst kind: we consider Tikhonov-Phillips regularization x = (A A + I) ?1 A y with a nite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires… (More)