In this paper, we propose a new primal-dual algorithm for minimizing f(x) + g(x) + h(Ax), where f , g, and h are convex functions, f is differentiable with a Lipschitz continuous gradient, and A is a bounded linear operator. It has some famous primal-dual algorithms for minimizing the sum of two functions as special cases. For example, it reduces to the Chambolle-Pock algorithm when f = 0 and a...

EEcient numerical schemes for nonlinear diiusion l-tering based on additive operator splitting (AOS) were introduced in 15]. AOS schemes are eecient and unconditionally stable, yet their accuracy is low. Future applications of nonlinear diiusion ltering may require additional accuracy at the expense of a relatively modest cost in computations and complexity. To investigate the eeect of higher a...

In this lecture, we discuss splitting algorithms for convex minimization problems with objective given by the sum of two nonsmooth functions. We start with the fixed point property of such problems and derive a general scheme of splitting algorithm based on fixed point iteration. This covers Douglas-Rachford splitting and Peaceman-Rachford splitting algorithms. We also discuss the convergence r...

This paper proposes novel metrics to evaluate the performance of object detection algorithms in video sequences. The proposed metrics allow to characterize the methods being used and classify the types of errors into region splitting, merging or merge-split, detection failures and false alarms. This methodology is applied to characterize the performance of five segmentation algorithms. These te...

This work examines several dynamical aspects of average consensus in mobile networks. The results herein allow consensus on general time-varying signals, and allow tracking analysis using standard frequency-domain techniques. Further, the frequency-domain analysis naturally inspires a robust small-gain version of the algorithm, which tolerates arbitrary non-uniform time delays. Finally, we show...

An effective non-local quantum field theory is constructed, which describes interaction of pomerons in the high-coloured QCD. The theory includes both splitting and merging triple pomeron vertexes and diagrams with pomeronic loops. The Schwinger-Dyson equations for the 'physical' pomeron are written. Conformal invariance allows to reduce the theory to the old-fashioned Gribov pomeron theory wit...