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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)

When using motion fields to interpolate between two consecutive images in an image sequence, a major problem is to handle occlusions and disclusions properly. However, in most cases, one of both images contains the information that is either discluded or occluded; if the first image contains the information (i.e., the region will be occluded), forward… (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)

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)

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. The functionals under consideration are the sum of a smooth, possibly non-convex and non-smooth, necessarily… (More)

—The number of available algorithms for the so-called Basis Pursuit Denoising problem (or the related LASSO-problem) is large and keeps growing. Similarly, the number of experiments to evaluate and compare these algorithms on different instances is growing. In this note, we present a method to produce instances with exact solutions which is based on a… (More)

The problem of finding a minimum ℓ<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 ℓ<sub>1</sub>-minimization, which often allows for early termination by “guessing” a… (More)