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Iteratively solving linear inverse problems under general convex constraints
We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algo- rithm that amounts to a projected Landweber iteration andExpand
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The Continuous Shearlet Transform in Arbitrary Space Dimensions
TLDR
A generalization of the continuous shearlet transform to higher dimensions using translations, anisotropic dilations and specific shear matrices. Expand
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Accelerated projected steepest descent method for nonlinear inverse problems with sparsity constraints
This paper is concerned with the construction of an iterative algorithm to solve nonlinear inverse problems with an l1 constraint on x. One extensively studied method to obtain a solution of such anExpand
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Shearlet coorbit spaces and associated Banach frames
Abstract In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to applyExpand
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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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Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum
TLDR
We propose a theory and set of methods for infinite-dimensional compressed sensing, or as we shall also refer to it, compressed sensing over the continuum. Expand
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Multi-frame representations in linear inverse problems with mixed multi-constraints
Abstract This paper is concerned with linear inverse problems where the solution is assumed to have a sparse expansion with respect to several bases or frames. We were mainly motivated by theExpand
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Generalized coorbit theory, Banach frames, and the relation to α-modulation spaces
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 thatExpand
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