of unknown transformations. For instance, images of a 3D object from varying viewpoints can be seen as the result of multiple nonlinear operators that act upon a small set of prototype views. Although this may seem like a non convex optimization problem, we propose a formulation that is convex and produces

Consider a dataset of vectors ~x1... ~xT on a low dimensional orbit manifold constructed by group actions.Here, actions mean a matrix acting on a data vector xt0 to map it to another xt via the exponentiatedmatrix product ~xt ss exp(At,t0)~xt0. We may consider mappings n = 1... N (where N = T 2) betweenall pairs of points t = 1... T and t0 = 1... T. Or, we may consider a subset of the T 2 mappings, i.e.choosing a single prototype by locking t0 = 1. Another choice is mapping points to their k nearestneighbors. Ultimately, we seek At,t0 matrices that faithfully reconstruct the data by minimizing the sumof reconstruction errors Et,t0(At,t0) j En(An) for any choice of N such mappings. This is like a regressionwhere input data has to regenerate itself as output. In addition to low reconstruction error, an important additional constraint on the transformation matrices An is that they themselves form a low dimensional subspace. This means only a few axes of freedom arepresent from the group actions or orbits. For instance, each

and performance analysis. The Circle and Popov criteria are used to obtain Lyapunov functions whose sublevel sets provide regions of guaranteed stability and performance within a restricted state space region. Our LMI formulation leads directly to simple convex optimization problems that can be solved efficiently

We present a system that is capable of interactively reconstructing a scene from a single live camera. We use a dense volumetric representation of the surface, which means there are no constraints concerning the 3D-scene topology. Reconstruction is based on range image fusion using a total

. The introduced method considers all three goals at the same time and produces higher quality output than existing methods. The technical contribution of our mapping is to derive a simplified convex optimization from a complex nonlinear optimization problem. During interactive visualization, we can map

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(FIR) FD filters. The problem will be posed as a convex optimization problem in which the maximum modulus of the complex error will be minized. Several design examples will be presented, along with an empirical formula for the filter order required to meet a given worst case group delay error

support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler-Raz equations and optimizing various constraints. Numerical experiments show that alternate dual windows with considerably improved features can be found. I.

Abstract—This work presents an application of convex op-timization and algebraic geometry in devising secure, power-efficient, beam-steerable, and on-chip transmission systems for wireless networks. First, we introduce a passively controllable smart (PCS) antenna system that can be programmed

Abstract not found