Learn More
The problem of the generation of an intermediate 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. This approach bears similarities with the Horn & Schunck method for optical flow calculation but in fact the model is quite different. The images are(More)
A new iterative algorithm for the solution of minimization problems in infinite-dimensional 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)
Minimization problems in ℓ 2 for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted ℓ 1 penalty term. The necessary and sufficient condition for optimality is shown to be slantly differentiable (Newton differentiable), hence a semismooth Newton method is applicable. Local superlinear convergence(More)
This paper addresses the regularization by sparsity constraints by means of weighted ℓ p penalties for 0 ≤ p ≤ 2. For 1 ≤ p ≤ 2 special attention is payed to convergence rates in norm and to source conditions. As main results it is proven that one gets a convergence rate of √ δ in the 2-norm for 1 < p ≤ 2 and in the 1-norm for p = 1 as soon as the unknown(More)
A new theorem on conditions for convergence to consensus of a multiagent time-dependent time-discrete 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)