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Orbit Learning using Convex Optimization
"... Recently, learning approaches have been brought to bear on nonlinear datasets by assuming samples lie on a lowdimensional Riemannian manifold in the embedding space. One solution is to model local variations linearly [1]. A fundamental difficulty with such solutions is they cannot extrapolate or ge ..."
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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
Orbit Learning using Convex Optimization
"... 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) bet ..."
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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
Analysis of Linear Systems with Saturation using Convex Optimization
 In Proceedings of 37th Conference on Decision and Control
, 1998
"... We show how Linear Matrix Inequalities (LMIs) can be used to perform local stability and performance analysis of linear systems with saturating elements. This leads to less conservative information on stability regions, disturbance rejection, and L 2  gain than standard global stability and perform ..."
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Cited by 36 (0 self)
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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
Online 3d reconstruction using convex optimization
 in 1st Workshop on Live Dense Reconstruction From Moving Cameras (ICCV
, 2011
"... 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 3Dscene topology. Reconstruction is based on range image fusion using a total variation ..."
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Cited by 16 (1 self)
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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 3Dscene topology. Reconstruction is based on range image fusion using a total
Interactive hyperspectral image visualization using convex optimization
 IEEE Trans. Geosci. Remote Sens
, 2009
"... Abstract—In this paper, we propose a new framework to visualize hyperspectral images. We present three goals for such a visualization: 1) preservation of spectral distances; 2) discriminability of pixels with different spectral signatures; 3) and interactive visualization for analysis. The introduce ..."
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Cited by 14 (2 self)
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. 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
Design of Fractional Delay Filters Using Convex Optimization
 IEEE Workshop on Appl. of Signal Processing to Audio and Acoustics
, 1997
"... Fractional sample delay (FD) filters are useful and necessary in many applications, such as the accurate steering of acoustic arrays [1], [2], delay lines for physical models of musical instruments [3] [4], and time delay estimation[5]. This paper addresses the design of finite impulse response (FIR ..."
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Cited by 10 (0 self)
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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
Gabor dual windows using convex optimization
"... Abstract—Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal `2norm dual window, is widely used. This window function however, might lack desirable properties, such as good timefrequency concentration, small suppor ..."
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Cited by 2 (1 self)
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support or smoothness. We employ convex optimization methods to design dual windows satisfying the WexlerRaz equations and optimizing various constraints. Numerical experiments show that alternate dual windows with considerably improved features can be found. I.
Programmable antenna design using convex optimization
 19th International Symposium on Mathematical Theory of Networks and Systems
, 2010
"... Abstract—This work presents an application of convex optimization and algebraic geometry in devising secure, powerefficient, beamsteerable, and onchip transmission systems for wireless networks. First, we introduce a passively controllable smart (PCS) antenna system that can be programmed to gen ..."
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Cited by 3 (3 self)
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Abstract—This work presents an application of convex optimization and algebraic geometry in devising secure, powerefficient, beamsteerable, and onchip transmission systems for wireless networks. First, we introduce a passively controllable smart (PCS) antenna system that can be programmed
Strategies for distributed sensor selection using convex optimization
 Proc. of IEEE GLOBECOM
, 2012
"... ar ..."
Results 1  10
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