distributed-ece-2009 - Distributed Compressive Sensing Dror...

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arXiv:0901.3403v1 [cs.IT] 22 Jan 2009 Distributed Compressive Sensing Dror Baron, 1 Marco F. Duarte, 2 Michael B. Wakin, 3 Shriram Sarvotham, 4 and Richard G. Baraniuk 2 1 Department of Electrical Engineering, Technion – Israel Institute of Technology, Haifa, Israel 2 Department of Electrical and Computer Engineering, Rice University, Houston, TX 3 Division of Engineering, Colorado School of Mines, Golden, CO 4 Halliburton, Houston, TX This paper is dedicated to the memory of Hyeokho Choi, our colleague, mentor, and friend. Abstract Compressive sensing is a signal acquisition framework based on the revelation that a small col- lection 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 en- ables 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 funda- mental 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. Keywords: Compressive sensing, distributed source coding, sparsity, random projection, random matrix, linear programming, array processing, sensor networks. 1 Introduction A core tenet of signal processing and information theory is that signals, images, and other data often contain some type of structure that enables intelligent representation and processing. The notion of structure has been characterized and exploited in a variety of ways for a variety of purposes. In this paper, we focus on exploiting signal correlations for the purpose of compression . This work was supported by the grants NSF CCF-0431150 and CCF-0728867, DARPA HR0011-08-1-0078, DARPA/ONR N66001-08-1-2065, ONR N00014-07-1-0936 and N00014-08-1-1112, AFOSR FA9550-07-1-0301, ARO MURI W311NF-07-1-0185, and the Texas Instruments Leadership University Program. Preliminary versions of this work have appeared at the Allerton Conference on Communication, Control, and Computing [1], the Asilomar Con- ference on Signals, Systems and Computers [2], the Conference on Neural Information Processing Systems [3], and the Workshop on Sensor, Signal and Information Processing [4].
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