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Linear Convergence of Iterative Soft-Thresholding
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate theExpand
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An Inertial Forward-Backward Algorithm for Monotone Inclusions
  • Dirk A. Lorenz, T. Pock
  • Mathematics, Computer Science
  • Journal of Mathematical Imaging and Vision
  • 14 March 2014
TLDR
We propose an inertial forward-backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. Expand
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Elastic-net regularization: error estimates and active set methods
This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l1 and l2Expand
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The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations
TLDR
We formulate this problem as a split feasibility problem, propose an algorithmic framework based on Bregman projections and prove a general convergence result for this framework. Expand
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Regularization with non-convex separable constraints
We consider regularization of nonlinear ill-posed problems with constraints which are non-convex. As a special case, we consider separable constraints, i.e. the regularization takes place in aExpand
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A semismooth Newton method for Tikhonov functionals with sparsity constraints
Minimization problems in l2 for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted l1 penalty term. The necessary and sufficientExpand
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A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing
TLDR
An algorithmic framework to compute sparse or minimal-TV solutions of linear systems is proposed. Expand
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Minimization of Non-smooth, Non-convex Functionals by Iterative Thresholding
TLDR
Convergence analysis is carried out for a forward-backward splitting/generalized gradient projection method for the minimization of a special class of non-smooth and genuinely non-convex minimization problems in infinite-dimensional Hilbert spaces. Expand
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Image Sequence Interpolation Using Optimal Control
TLDR
In this paper we modify the model proposed in [10] for interpolating intermediate images between two given images in an image sequence and analyze the well-posedness of the corresponding minimizing problem. Expand
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Iterated Hard Shrinkage for Minimization Problems with Sparsity Constraints
TLDR
A new iterative algorithm for the solution of minimization problems in infinite-dimensional Hilbert spaces which involve sparsity constraints in form of $\ell^{p}$-penalties is proposed. Expand
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