arXiv subjects

Dror Baron

Publications and source records attributed to Dror Baron.

57 records · Page 4Linked to original sources

arXiv2011

Fault Identification via Non-parametric Belief Propagation

We consider the problem of identifying a pattern of faults from a set of noisy linear measurements. Unfortunately, maximum a posteriori probability estimation of the fault pattern is computationally intractable. To solve the fault identification problem, we propose a non-parametric belief propagation approach. We show empirically that our belief propagation solver is more accurate than recent state-of-the-art algorithms including interior point methods and semidefinite programming. Our superior performance is explained by the fact that we take into account both the binary nature of the individual faults and the sparsity of the fault pattern arising from their rarity.

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arXiv2009

Bayesian Compressive Sensing via Belief Propagation

Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform approximate Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length-N signal containing K large coefficients, our CS-BP decoding algorithm uses O(Klog(N)) measurements and O(Nlog^2(N)) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models.

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arXiv2009

Distributed Compressive Sensing

Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for distributed compressive sensing (DCS) that enables new distributed coding algorithms for multi-signal ensembles that exploit both intra- and inter-signal correlation structures. The DCS theory rests on a new concept that we term the joint sparsity of a signal ensemble. Our theoretical contribution is to characterize the fundamental performance limits of DCS recovery for jointly sparse signal ensembles in the noiseless measurement setting; our result connects single-signal, joint, and distributed (multi-encoder) compressive sensing. To demonstrate the efficacy of our framework and to show that additional challenges such as computational tractability can be addressed, we study in detail three example models for jointly sparse signals. For these models, we develop practical algorithms for joint recovery of multiple signals from incoherent projections. In two of our three models, the results are asymptotically best-possible, meaning that both the upper and lower bounds match the performance of our practical algorithms. Moreover, simulations indicate that the asymptotics take effect with just a moderate number of signals. DCS is immediately applicable to a range of problems in sensor arrays and networks.

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