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Jun 30, 2018
06/18

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João F. C. Mota; Nikos Deligiannis; Miguel R. D. Rodrigues

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We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via L1-L1 and L1-L2 minimization. We then provide lower bounds on the number of measurements that these problems require for successful reconstruction of the target signal. If the side information has good quality, the number of measurements is significantly reduced...

Topics: Statistics, Mathematics, Computing Research Repository, Information Theory, Machine Learning,...

Source: http://arxiv.org/abs/1410.2724

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10.0

Jun 28, 2018
06/18

by
Nikos Deligiannis; Joao F. C. Mota; George Smart; Yiannis Andreopoulos

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Distributed desynchronization algorithms are key to wireless sensor networks as they allow for medium access control in a decentralized manner. In this paper, we view desynchronization primitives as iterative methods that solve optimization problems. In particular, by formalizing a well established desynchronization algorithm as a gradient descent method, we establish novel upper bounds on the number of iterations required to reach convergence. Moreover, by using Nesterov's accelerated gradient...

Topics: Systems and Control, Optimization and Control, Multiagent Systems, Information Theory, Computing...

Source: http://arxiv.org/abs/1507.06239

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4.0

Jun 30, 2018
06/18

by
Joao F. C. Mota; Nikos Deligiannis; Miguel R. D. Rodrigues

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We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via L1-L1 and L1-L2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruct the original signal. Our bounds and geometrical interpretations reveal that if the prior information...

Topics: Mathematics, Computing Research Repository, Information Theory

Source: http://arxiv.org/abs/1408.5250

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6.0

Jun 29, 2018
06/18

by
Nikos Deligiannis; João F. C. Mota; Bruno Cornelis; Miguel R. D. Rodrigues; Ingrid Daubechies

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In support of art investigation, we propose a new source sepa- ration method that unmixes a single X-ray scan acquired from double-sided paintings. Unlike prior source separation meth- ods, which are based on statistical or structural incoherence of the sources, we use visual images taken from the front- and back-side of the panel to drive the separation process. The coupling of the two imaging modalities is achieved via a new multi-scale dictionary learning method. Experimental results...

Topics: Computer Vision and Pattern Recognition, Computing Research Repository

Source: http://arxiv.org/abs/1605.06474

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Sep 24, 2013
09/13

by
João F. C. Mota; João M. F. Xavier; Pedro M. Q. Aguiar; Markus Püschel

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We give a general proof of convergence for the Alternating Direction Method of Multipliers (ADMM). ADMM is an optimization algorithm that has recently become very popular due to its capabilities to solve large-scale and/or distributed problems. We prove that the sequence generated by ADMM converges to an optimal primal-dual optimal solution. We assume the functions f and g, defining the cost f(x) + g(y), are real-valued, but constrained to lie on polyhedral sets X and Y. Our proof is an...

Source: http://arxiv.org/abs/1112.2295v1

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Sep 23, 2013
09/13

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João F. C. Mota; João M. F. Xavier; Pedro M. Q. Aguiar; Markus Püschel

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We propose a distributed algorithm, named Distributed Alternating Direction Method of Multipliers (D-ADMM), for solving separable optimization problems in networks of interconnected nodes or agents. In a separable optimization problem there is a private cost function and a private constraint set at each node. The goal is to minimize the sum of all the cost functions, constraining the solution to be in the intersection of all the constraint sets. D-ADMM is proven to converge when the network is...

Source: http://arxiv.org/abs/1202.2805v2

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Sep 19, 2013
09/13

by
João F. C. Mota; João M. F. Xavier; Pedro M. Q. Aguiar; Markus Püschel

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We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction. Our algorithm solves BP on a distributed platform such as a sensor network, and is designed to minimize the communication between nodes. The algorithm only requires the network to be connected, has no notion of a central processing node, and no node has...

Source: http://arxiv.org/abs/1009.1128v3

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Jun 29, 2018
06/18

by
Nikos Deligiannis; Joao F. C. Mota; Bruno Cornelis; Miguel R. D. Rodrigues; Ingrid Daubechies

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In support of art investigation, we propose a new source separation method that unmixes a single X-ray scan acquired from double-sided paintings. In this problem, the X-ray signals to be separated have similar morphological characteristics, which brings previous source separation methods to their limits. Our solution is to use photographs taken from the front and back-side of the panel to drive the separation process. The crux of our approach relies on the coupling of the two imaging modalities...

Topics: Computer Vision and Pattern Recognition, Computing Research Repository

Source: http://arxiv.org/abs/1607.04147

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Jun 27, 2018
06/18

by
Joao F. C. Mota; Nikos Deligiannis; Aswin C. Sankaranarayanan; Volkan Cevher; Miguel R. D. Rodrigues

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We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear dynamical model. Our algorithm, based on recent theoretical results for $\ell_1$-$\ell_1$ minimization, is recursive and computes the number of measurements to be taken at each time on-the-fly. As an example, we apply the algorithm to compressive video...

Topics: Machine Learning, Statistics, Computer Vision and Pattern Recognition, Optimization and Control,...

Source: http://arxiv.org/abs/1503.03231