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We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber iteration and that provides and iterative approach to the solution of this inverse problem. For relatively moderate assumptions on the constraint we can always prove weak… (More)

- G. Teschke, I. Daubechies
- 2004

Inspired by papers of Vese–Osher [OV02] and Osher–Solé–Vese [OSV02] we present a wavelet–based treatment of variational problems arising in the field of image processing. In particular, we follow their approach and discuss a special class of variational functionals that induce a decomposition of images into oscillating and cartoon components and possibly an… (More)

- V. Lehmann, G. Teschke
- 2001

In this paper, we apply wavelet thresholding for removing automatically ground and intermittent clutter (airplane echoes) from wind profiler radar data. Using the concept of discrete multi-resolution analysis and non-parametric estimation theory, we develop wavelet domain thresholding rules, which allow us to identify the coefficients relevant for clutter… (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)

- 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)

This paper is concerned with the construction of an iterative algorithm to solve non-linear inverse problems with an 1 constraint. One extensively studied method to obtain a solution of such an 1 penalized problem is iterative soft-thresholding. Regrettably, such iteration schemes are computationally very intensive. A subtle alternative to iterative… (More)

- Ben Adcock, Anders C. Hansen, Evelyn Herrholz, Gerd Teschke
- 2011

Generalized sampling is new framework for sampling and reconstruction in infinite-dimensional Hilbert spaces. Given measurements (inner products) of an element with respect to one basis, it allows one to reconstruct in another, arbitrary basis, in a way that is both convergent and numerically stable. However, generalized sampling is thus far only valid for… (More)

Finding optimal representations of signals in higher dimensions, in particular directional representations, is currently the subject of intensive research. Since it might be difficult to obtain directional information by means of wavelets, several new representation systems were proposed in the past, including ridgelets, curvelets and, more recently,… (More)

- Evelyn Herrholz, Gerd Teschke
- 2010

In this paper we shall be concerned with compressive sampling strategies and sparse recovery principles for linear inverse and ill-posed problems. As the main result, we provide compressed measurement models for ill-posed problems and recovery accuracy estimates for sparse approximations of the solution of the underlying inverse problem. The main… (More)

- PISAMAI KITTIPOOM, Stephan Dahlke, Christopher Heil, Demetrio Labate, Gabriele Steidl, Gerd Teschke
- 2010

Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few construction strategies for discrete shearlet systems are known so far. In this paper, we take a geometric approach to this… (More)