Gerd Teschke

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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)
This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Similar to the twodimensional case, our approach is based on translations, anisotropic dilations and specific shear matrices. We show that the associated integral transform again originates from a square-integrable representation of a specific group,(More)
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)
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)
This paper is concerned with the construction of an iterative algorithm to solve nonlinear 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)
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)
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 generalizations and specific applications of the coorbit space theory based on group representations modulo quotients that has been developed quite recently. We show that the general theory applied to the affine Weyl–Heisenberg group gives rise to families of smoothness spaces that can be identified with α-modulation spaces.
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)