Distributed Compressive Sensing

By Dror Baron, Michael B. Wakin, Marco F. Duarte, Shriram Sarvotham, Richard Baraniuk. arXiv.org, 2009

568 citations recorded by the source corpus.

Abstract : 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.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/773c5c6a135b4082f735054c14960210c06ec54a

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Citations in the corpus

Compressive Radar Imaging (2007, background): “Our results can also be combined with the theory of distributed compressed sensing (DCS) [11], [12] for array processing and beamforming type applications.”
Sure independence screening for ultrahigh dimensional feature space (2006, unknown): “We would like to point out that the Simple Thresholding Algorithm (see, e.g., Baron et al. , 2005 and Gribonval et al. , 2007) that is used in sparse approximation or compressed sensing is a one step greedy algorithm and related to SIS.”
Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors (2008, background): “The result of Theorem 3 resembles a result of [23], in which the authors suggested merging the columns of Y using an ordinary summation.”
An Introduction To Compressive Sampling (2008, background): “Original Signal Versus Reconstruction x x * IEEE SIGNAL PROCESSING MAGAZINE [27] MARCH 2008 This proves that one can stably and accurately reconstruct nearly sparse signals from dramatically undersampled data in an incoherent domain.”
A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data (2010, background): “Given that is acquired from a highly sparse signal, a reasonable approach would be to seek the sparsest one among all the solutions of (2), i.e., (3) Decoder (3) is able to recover a -sparse signal exactly with overwhelming probability using only i.i.d. Gaussian measurements [3].”
A Proximal Gradient Algorithm for Decentralized Composite Optimization (2015, background): “The decentralized compressed sensing is a special case of the general distributed compressed sensing [35] where its intrasignal correlation is consensus.”
An Architecture for Compressive Imaging (2006, unknown): “Although only K + 1 measurements are required to recover sparse signals via fo optimization [7], with Basis Pursuit one typically requires M > cK measurements, where c > 1 is an overmeasuring factor.”
Enhancing Sparsity by Reweighted ℓ1 Minimization (2007, background): “The implications of these facts are quite far-reaching, with potential applications in data compression [24, 28], digital photography [29], medical imaging [23, 30], error correction [31, 32], analog-todigital conversion [33], sensor networks [34, 35], and so on.”
Compressive Sensing [Lecture Notes] (2007, background): “…consider the 0 norm that counts the number of non-zero entries in s. (Hence a K -sparse vector has 0 norm equal to K.) The modified opti- mization s = argmin s 0 such that s = y (5) can recover a K-sparse signal exactly with high probability using only M = K + 1 iid Gaussian measurements [5].”
Group sparse optimization by alternating direction method (2013, background): “Jointly sparse solutions, namely, a set of sparse solutions that share a common nonzero support, arise in cognitive radio networks [19], distributed compressive sensing [20], direction-of-arrival estimation in radar [21], magnetic resonance imaging with multiple coils [22] and many other application”
Random Projections of Smooth Manifolds (2009, background): “Interestingly, the number 2K also arises in CS as the number of random measurements required to embed the set of all K-sparse signals (but again with no guarantee on the conditioning of the recovery problem); see [3].”
Distributed Compressed Sensing of Jointly Sparse Signals (2005, unknown): “prising result, which is proved in [7] .”
Multi-task compressive sensing with Dirichlet process priors (2008, methodology): “||l1 , s.t., v = <., (1) if the number of CS measurements n>C N log m (C is a small constant); if N is small (i.e., if u is highly compressible in the basis G) then n « m.”
Distributed Compressive CSIT Estimation and Feedback for FDD Multi-User Massive MIMO Systems (2014, methodology): “However, the joint sparsity structure in our multi-user massive MIMO scenario is much more complicated and is not covered by these existing models [21] and hence, the associated recovery algorithms cannot be extended to our scenario.”
Distributed Multi-Task Learning (2015, background): “[19] propose a “group orthogonal matching pursuit”-type algorithm.”
Average Case Analysis of Multichannel Sparse Recovery Using Convex Relaxation (2009, unknown): “In [2], the buzzword distributed compressed sensing was coined for this setup.”
Alternating Direction Algorithms for 1-Problems in Compressive Sensing (2009, background): “Indeed, with overwhelming probability decoder (1.2) can recover sparse signals exactly from a very limited number of random measurements (see e.g., [1]).”
Model-Based Compressive Sensing (2008, methodology): “An equivalent problem arises in CS for signal ensembles, such as sensor networks and MIMO c ommunication [8, 9, 34].”