nips nips2005 nips2005-163 nips2005-163-reference knowledge-graph by maker-knowledge-mining
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Author: Michael B. Wakin, Marco F. Duarte, Shriram Sarvotham, Dror Baron, Richard G. Baraniuk
Abstract: Compressed sensing is an emerging field based on the revelation that a small group of linear projections of a sparse signal contains enough information for reconstruction. In this paper we introduce a new theory for distributed compressed 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. We study three simple models for jointly sparse signals, propose algorithms for joint recovery of multiple signals from incoherent projections, and characterize theoretically and empirically the number of measurements per sensor required for accurate reconstruction. In some sense DCS is a framework for distributed compression of sources with memory, which has remained a challenging problem in information theory for some time. DCS is immediately applicable to a range of problems in sensor networks and arrays. 1
[1] D. Baron, M. F. Duarte, S. Sarvotham, M. B. Wakin, and R. G. Baraniuk. An informationtheoretic approach to distributed compressed sensing. In Allerton Conf. Comm., Control, Comput., Sept. 2005.
[2] D. Baron, M. B. Wakin, M. F. Duarte, S. Sarvotham, and R. G. Baraniuk. Distributed compressed sensing. 2005. Preprint. Available at www.dsp.rice.edu/cs.
[3] E. Cand` s, J. Romberg, and T. Tao. Stable signal recovery from incomplete and inaccurate e measurements. Comm. Pure Applied Mathematics, 2005. To appear.
[4] E. Cand` s and T. Tao. Near optimal signal recovery from random projections and universal e encoding strategies. 2004. Preprint.
[5] E. Cand` s and T. Tao. The Dantzig selector: Statistical estimation when p is much larger than e n. 2005. Preprint.
[6] E. Cand` s and T. Tao. Error correction via linear programming. 2005. Preprint. e
[7] S. Chen, D. Donoho, and M. Saunders. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20(1):33–61, 1998.
[8] T. M. Cover and J. A. Thomas. Elements of Information Theory. Wiley, New York, 1991.
[9] D. Donoho. Compressed sensing. 2004. Preprint.
[10] D. Donoho and Y. Tsaig. Extensions of compressed sensing. 2004. Preprint.
[11] M. F. Duarte, S. Sarvotham, D. Baron, M. B. Wakin, and R. G. Baraniuk. Distributed compressed sensing of jointly sparse signals. In Asilomar Conf. Signals, Sys., Comput., Nov. 2005.
[12] J. Haupt and R. Nowak. Signal reconstruction from noisy random projections. 2005. Preprint.
[13] S. Pradhan and K. Ramchandran. Distributed source coding using syndromes (DISCUS): Design and construction. IEEE Trans. Inform. Theory, 49:626–643, March 2003.
[14] D. Slepian and J. K. Wolf. Noiseless coding of correlated information sources. IEEE Trans. Inform. Theory, 19:471–480, July 1973.
[15] J. Tropp and A. C. Gilbert. Signal recovery from partial information via orthogonal matching pursuit. 2005. Preprint.
[16] J. Tropp, A. C. Gilbert, and M. J. Strauss. Simulataneous sparse approximation via greedy pursuit. In IEEE 2005 Int. Conf. Acoustics, Speech, Signal Processing, March 2005.
[17] Z. Xiong, A. Liveris, and S. Cheng. Distributed source coding for sensor networks. IEEE Signal Proc. Mag., 21:80–94, September 2004.