Dirk A. Lorenz

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The problem of finding an interpolating image between two given images in an image sequence is considered. The problem is formulated as an optimal control problem governed by a transport equation, i.e. we aim at finding a flow field which transports the first image as close as possible to the second image. This approach bears similarities with the Horn and(More)
Numerical algorithms for a special class of non-smooth and non-convex minimization problems in infinite dimensional Hilbert spaces are considered. The functionals under consideration are the sum of a smooth and non-smooth functional, both possibly non-convex. We propose a generalization of the gradient projection method and analyze its convergence(More)
In this paper, 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. The algorithm is inspired by the accelerated gradient method of Nesterov, but can be applied to a much larger class of problems including convex-concave saddle point problems and(More)
A new iterative algorithm for the solution of minimization problems in infinitedimensional Hilbert spaces which involve sparsity constraints in form of `p-penalties is proposed. In contrast to the well-known algorithm considered by Daubechies, Defrise and De Mol, it uses hard instead of soft shrinkage. It is shown that the hard shrinkage algorithm is a(More)
The problem of finding a minimum &ell;<sub>1</sub>-norm solution to an underdetermined linear system is an important problem in compressed sensing, where it is also known as <i>basis pursuit</i>. We propose a heuristic optimality check as a general tool for &ell;<sub>1</sub>-minimization, which often allows for early termination by &#8220;guessing&#8221; a(More)
Inline digital holograms are classically reconstructed using linear operators to model diffraction. It has long been recognized that such reconstruction operators do not invert the hologram formation operator. Classical linear reconstructions yield images with artifacts such as distortions near the field-of-view boundaries or twin images. When objects(More)
A new theorem on conditions for convergence to consensus of a multiagent time-dependent timediscrete dynamical system is presented. The theorem is build up on the notion of averaging maps. We compare this theorem to Moreau’s Theorem and his proposed set-valued Lyapunov theory (IEEE Transactions on Automatic Control, vol. 50, no. 2, 2005). We give examples(More)