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## Distributed compressed sensing (2005)

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Citations: | 135 - 26 self |

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12168 |
Elements of Information Theory
- Cover, Thomas
(Show Context)
Citation Context ...buted coding of so-called “sources with memory.” (We briefly mention some limitations here and elaborate in Section 2.1.3.) The direct implementation for such sources would require huge lookup tables =-=[13, 25]-=-. Furthermore, approaches combining pre- or post-processing of the data to remove intra-signal correlations combined with Slepian-Wolf coding for the inter-signal correlations appear to have limited a... |

3542 | Compressed sensing
- Donoho
- 2006
(Show Context)
Citation Context ...ed in Theorem 10 involves combinatorial searches for estimating the innovation components. More efficient techniques could also be employed (including several proposed for CS in the presence of noise =-=[38, 39, 45, 48, 51]-=-). It is reasonable to expect similar behavior; as the error in estimating the common component diminishes, these techniques should perform similarly to their noiseless analogues (Basis Pursuit [45, 4... |

3136 |
A Wavelet Tour of Signal Processing
- Mallat
- 1998
(Show Context)
Citation Context ...orm coefficients can be transmitted or stored rather than N ≫ K signal samples. For example, smooth signals are sparse in the Fourier basis, and piecewise smooth signals are sparse in a wavelet basis =-=[7]-=-; the commercial coding standards MP3 [8], JPEG [9], and JPEG2000 [10] directly exploit this sparsity. 1.1 Distributed source coding While the theory and practice of compression have been well develop... |

2681 | Atomic decomposition by basis pursuit
- Chen, Donoho, et al.
- 1998
(Show Context)
Citation Context ...he vertical axis indicates the probability that the linear program yields the correct answer x as a function of the oversampling factor c = M/K. This optimization problem, also known as Basis Pursuit =-=[51]-=-, is significantly more approachable and can be solved with traditional linear programming techniques whose computational complexities are polynomial in N. There is no free lunch, however; according t... |

2559 | Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Candès, Romberg, et al.
- 2006
(Show Context)
Citation Context ...ng (CS) A new framework for single-signal sensing and compression has developed recently under the rubric of Compressed Sensing (CS). CS builds on the ground-breaking work of Candès, Romberg, and Tao =-=[27]-=- and Donoho [28], who showed that if a signal has a sparse representation in one basis then it can be recovered from a small number of projections onto a second basis that is incoherent with the first... |

1728 | Near Shannon limit error correcting coding and decoding: Turbo-codes
- Berrou, Glavieux
- 1996
(Show Context)
Citation Context ...n to match across signals — as in JSM-2 — then more powerful algorithms like SOMP can be used. The ACIE algorithm is similar in spirit to other iterative estimation algorithms, such as turbo decoding =-=[65]-=-. 5.3.3 Simulations for JSM-3 We now present simulations of JSM-3 recovery for the following scenario. Consider J signals of length N = 50 containing a common white noise component zC(n) ∼ N(0,1) for ... |

1510 | Embedded image coding using zerotrees of wavelet coefficients - Shapiro - 1993 |

1476 | Practical signal recovery from random projections
- Candès, Romberg
- 2005
(Show Context)
Citation Context ...versal in the sense that the sensor can apply the same measurement mechanism no matter what basis the signal is sparse in (and thus the coding algorithm is independent of the sparsity-inducing basis) =-=[28, 29]-=-. While powerful, the CS theory at present is designed mainly to exploit intra-signal structures at a single sensor. To the best of our knowledge, the only work to date that applies CS in a multisenso... |

1402 | An introduction to compressive sampling
- Candes, Wakin
- 2008
(Show Context)
Citation Context ...e single-signal CS literature that we should be able to leverage, including variants of Basis Pursuit with Denoising [63, 69], robust iterative recovery algorithms [64], CS noise sensitivity analysis =-=[25, 34]-=-, the Dantzig Selector [33], and one-bit CS [70]. Third, in some applications, the linear program associated with some DCS decoders (in JSM-1 and JSM-3) could prove too computationally intense. As we ... |

1367 | Decoding by linear programming - Candes, Tao - 2005 |

1360 | Stable signal recovery from incomplete and inaccurate information
- Candes, Romberg, et al.
(Show Context)
Citation Context ...ed in Theorem 10 involves combinatorial searches for estimating the innovation components. More efficient techniques could also be employed (including several proposed for CS in the presence of noise =-=[38, 39, 45, 48, 51]-=-). It is reasonable to expect similar behavior; as the error in estimating the common component diminishes, these techniques should perform similarly to their noiseless analogues (Basis Pursuit [45, 4... |

1298 |
Introduction to Graph Theory
- West
- 2004
(Show Context)
Citation Context ...note the single node matched to k by an edge in E, and we set C(k) = j. To prove the existence of such a matching within the graph, we invoke a version of Hall’s marriage theorem for bipartite graphs =-=[71]-=-. Hall’s theorem states that within a bipartite graph (V1,V2,E), there exists a matching that assigns each element of V1 to a unique element of V2 if for any collection of elements Π ⊆ V1, the set E(Π... |

1247 |
Noiseless coding of correlated information sources
- Slepian, Wolf
(Show Context)
Citation Context ... j � (14) Mj ≥ K ′ j + K∩ + 1, j = 1,2,... ,J, (15a) Mj ≥ K ′ C + � j 21 K ′ j + J · K∩ + 1. (15b)sThe measurement rates required in Theorem 4 are somewhat similar to those in the SlepianWolf theorem =-=[14]-=-, where each signal must be encoded above its conditional entropy rate, and the entire collection must be coded above the joint entropy rate. In particular, we see that the measurement rate bounds ref... |

931 |
Wireless integrated network sensors
- Pottie, Kaiser
- 2000
(Show Context)
Citation Context ...y large number of distributed sensor nodes can be programmed to perform a variety of data acquisition tasks as well as to network themselves to communicate their results to a central collection point =-=[11, 12]-=-. In many sensor networks, and in particular battery-powered ones, communication energy and bandwidth are scarce resources; both factors make the reduction of communication critical. Fortunately, sinc... |

856 | The Dantzig selector: statistical estimation when p is much larger than n
- Candès, Tao
- 2007
(Show Context)
Citation Context ...rformance. For example, the measurements will typically be real numbers that must be quantized and encoded, which will gradually degrade the reconstruction quality as the quantization becomes coarser =-=[39]-=- (see also Section 7). Characterizing DCS in light of practical considerations such as rate-distortion tradeoffs, power consumption in sensor networks, etc., are topics of ongoing research [40]. 1.5 P... |

747 | Cosamp: Iterative signal recovery from incomplete and inaccurate samples
- Needell, Tropp
- 2009
(Show Context)
Citation Context ...al from incoherent measurements with high probability, at the expense of slightly more measurements, [26, 43]. Algorithms inspired by OMP, such as regularized orthogonal matching pursuit [44], CoSaMP =-=[45]-=-, and Subspace Pursuit [46] have been shown to attain similar guarantees to those of their optimization-based counterparts. In the following, we will exploit both Basis Pursuit and greedy algorithms f... |

671 | Compressive sensing
- Baraniuk
- 2007
(Show Context)
Citation Context ...pt is that the ordering of these coefficients is important. For JSM-2, we can extend the notion of simultaneous sparsity for ℓp-sparse signals whose sorted coefficients obey roughly the same ordering =-=[66]-=-. This condition could perhaps be enforced as an ℓp constraint on the composite signal ⎧ ⎫ ⎨ J∑ J∑ J∑ ⎬ |xj(1)|, |xj(2)|, ..., |xj(N)| ⎩ ⎭ . j=1 j=1 Second, (random) measurements are real numbers; qua... |

621 | A simple proof of the restricted isometry property for random matrices
- Baraniuk, Davenport, et al.
(Show Context)
Citation Context ... that is incoherent with all others. Hence, when using a random basis, CS is universal in the sense that the sensor can apply the same measurement mechanism no matter what basis sparsifies the signal =-=[27]-=-. While powerful, the CS theory at present is designed mainly to exploit intra-signal structures at a single sensor. In a multi-sensor setting, one can naively obtain separate measurements from each s... |

403 | Distributed source coding using syndromes (DISCUS): Design and construction
- Pradhan, Ramchandran
- 1999
(Show Context)
Citation Context ...as the distinct advantage that the sensors need not collaborate while encoding their measurements, which saves valuable communication overhead. Unfortunately, however, most existing coding algorithms =-=[15, 16]-=- exploit only inter-signal correlations and not intra-signal correlations. To date there has been only limited progress on distributed coding of so-called “sources with memory.” (We briefly mention so... |

389 | Curvelets: a surprisingly effective nonadaptive representationof objects with edges
- Candès, Donoho
- 1999
(Show Context)
Citation Context ...e ℓp norm, 5 we can write that �θ�0 = K. Various expansions, including wavelets [7], Gabor bases [7], 5 The ℓ0 “norm” �θ�0 merely counts the number of nonzero entries in the vector θ. 8 ℓ=1scurvelets =-=[43]-=-, etc., are widely used for representation and compression of natural signals, images, and other data. In this paper, we will focus on exactly K-sparse signals and defer discussion of the more general... |

365 | Image compression through wavelet transform coding - DeVore, Jawerth, et al. - 1992 |

357 | Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit
- Tropp, Gilbert, et al.
- 2006
(Show Context)
Citation Context ... our DCS framework. SOMP is a variant of OMP that seeks to identify Ω one element at a time. (A similar 31ssimultaneous sparse approximation algorithm has been proposed using convex optimization; see =-=[57]-=- for details.) We dub the DCS-tailored SOMP algorithm DCS-SOMP. To adapt the original SOMP algorithm to our setting, we first extend it to cover a different measurement basis Φj for each signal xj. Th... |

350 |
Connecting the physical world with pervasive networks
- Estrin, Culler, et al.
- 2002
(Show Context)
Citation Context ...y large number of distributed sensor nodes can be programmed to perform a variety of data acquisition tasks as well as to network themselves to communicate their results to a central collection point =-=[11, 12]-=-. In many sensor networks, and in particular battery-powered ones, communication energy and bandwidth are scarce resources; both factors make the reduction of communication critical. Fortunately, sinc... |

269 | Sparse solutions to linear inverse problems with multiple measurement vectors
- Cotter, Rao, et al.
- 2005
(Show Context)
Citation Context ...rocessing algorithms. Another useful application for JSM-2 is MIMO communication [34]. Similar signal models have been considered by different authors in the area of simultaneous sparse approximation =-=[34, 52, 53]-=-. In this setting, a collection of sparse signals share the same expansion vectors from a redundant dictionary. The sparse approximation can be recovered via greedy algorithms such as Simultaneous Ort... |

254 |
still image data compression standard
- Pennebaker, Mitchell
- 1992
(Show Context)
Citation Context ...r than N ≫ K signal samples. For example, smooth signals are sparse in the Fourier basis, and piecewise smooth signals are sparse in a wavelet basis [7]; the commercial coding standards MP3 [8], JPEG =-=[9]-=-, and JPEG2000 [10] directly exploit this sparsity. 1.1 Distributed source coding While the theory and practice of compression have been well developed for individual signals, many applications involv... |

239 | Signal reconstruction fromnoisy randomprojections
- Haupt, NowakR
(Show Context)
Citation Context ...ry at present is designed mainly to exploit intra-signal structures at a single sensor. To the best of our knowledge, the only work to date that applies CS in a multisensor setting is Haupt and Nowak =-=[38]-=- (see Section 2.2.6). However, while their scheme exploits inter-signal correlations, it ignores intra-signal correlations. 1.3 Distributed compressed sensing (DCS) In this paper we introduce a new th... |

218 | Distributed source coding for sensor networks
- Xiong, Liveris, et al.
- 2004
(Show Context)
Citation Context ...as the distinct advantage that the sensors need not collaborate while encoding their measurements, which saves valuable communication overhead. Unfortunately, however, most existing coding algorithms =-=[15, 16]-=- exploit only inter-signal correlations and not intra-signal correlations. To date there has been only limited progress on distributed coding of so-called “sources with memory.” (We briefly mention so... |

189 | Signal recovery from partial information via orthogonal matching pursuit
- Tropp, Gilbert
- 2005
(Show Context)
Citation Context ...e of slightly more measurements, iterative greedy algorithms have also been developed to recover the signal x from the measurements y. Examples include the iterative Orthogonal Matching Pursuit (OMP) =-=[30]-=-, matching pursuit (MP), and tree matching pursuit (TMP) [35, 36] algorithms. OMP, for example, iteratively selects the vectors from the holographic basis ΦΨ that contain most of the energy of the mea... |

178 | Quantitative robust uncertainty principles and optimally sparse decompositions - Candés, Romberg |

177 | SpaceFrequency Quantization for Wavelet Image Coding - Xiong, Ramchandran, et al. - 1997 |

160 |
PRISM: A New Robust Video Coding Architecture Based on Distributed Compression Principles
- Puri, Ramchandran
- 2002
(Show Context)
Citation Context ...he advantage of moving the bulk of the computational complexity to the video decoder. Puri and Ramchandran have proposed a similar scheme based on Wyner-Ziv distributed encoding in their PRISM system =-=[54]-=-. In general, JSM-3 may be invoked for ensembles with significant inter-signal correlations but insignificant intra-signal correlations. 3.4 Refinements and extensions Each of the JSMs proposes a basi... |

134 | Recovery of exact sparse representations in the presence of bounded noise
- Fuchs
- 2005
(Show Context)
Citation Context ...istortion consequences in the DCS setting are topics for future work, there has been work in the single-signal CS literature that we should be able to leverage, including Basis Pursuit with Denoising =-=[28, 45, 51, 58]-=-, robust iterative reconstruction algorithms [38], CS noise sensitivity analysis [27], and the Dantzig Selector [39]. Fast algorithms: In some applications, the linear program associated with some DCS... |

130 |
A proof of the data compression theorem of Slepian and Wolf for ergodic sources
- Cover
- 1975
(Show Context)
Citation Context ...buted coding of so-called “sources with memory.” (We briefly mention some limitations here and elaborate in Section 2.1.3.) The direct implementation for such sources would require huge lookup tables =-=[13, 25]-=-. Furthermore, approaches combining pre- or post-processing of the data to remove intra-signal correlations combined with Slepian-Wolf coding for the inter-signal correlations appear to have limited a... |

127 | Modelling data-centric routing in wireless sensor networks - Krishnamachari, Estrin, et al. - 2002 |

120 | On network correlated data gathering - Cristescu, Beferull-Lozano, et al. - 2004 |

117 |
Coding Theorems of Information Theory
- Wolfowitz
- 1978
(Show Context)
Citation Context ... per-symbol rate that enables lossless compression. Various techniques such as arithmetic coding [13] can be used to compress near the entropy rate. 2.1.2 Distributed source coding Information theory =-=[13, 17]-=- has also provided tools that characterize the performance of distributed source coding. For correlated length-N sequences x1 and x2 generated by sources X1 and X2 over discrete alphabets X1 and X2, w... |

117 |
High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
- Donoho
(Show Context)
Citation Context ...early the probability increases with the number of measurements M = cK. Moreover, the curves become closer to a step function as N grows. In an illuminating series of recent papers, Donoho and Tanner =-=[32, 33]-=- have characterized the oversampling factor c(S) precisely. With appropriate oversampling, reconstruction via Basis Pursuit is also provably robust to measurement noise and quantization error [27]. In... |

110 | Recovery algorithms for vector valued data with joint sparsity constraints
- Fornassier, Rauhut
- 2008
(Show Context)
Citation Context ...k [47] and to the continuous-time setting [48]. Since the original submission of this paper, additional work has focused on the analysis and proposal of recovery algorithms for jointly sparse signals =-=[49, 50]-=-. 3 Joint Sparsity Signal Models In this section, we generalize the notion of a signal being sparse in some basis to the notion of an ensemble of signals being jointly sparse. 3.1 Notation We will use... |

101 | Error correction via linear programming
- Candés, Rudelson, et al.
- 2005
(Show Context)
Citation Context ...ving this ℓ0 optimization problem is prohibitively complex, requiring a combinatorial enumeration of the � � N K possible sparse subspaces. In fact, the ℓ0-recovery problem is known to be NP-complete =-=[31]-=-. Yet another challenge is robustness; in the setting of Theorem 2, the recovery may be very poorly conditioned. In fact, both of these considerations (computational complexity and robustness) can be ... |

99 | Reduce and boost: Recovering arbitrary sets of jointly sparse vectors
- Mishali, Eldar
- 2008
(Show Context)
Citation Context ...structure and that exploit both inter- and intra-signal correlations. Recent work has adapted DCS to the finite rate of innovation signal acquisition framework [47] and to the continuous-time setting =-=[48]-=-. Since the original submission of this paper, additional work has focused on the analysis and proposal of recovery algorithms for jointly sparse signals [49, 50]. 3 Joint Sparsity Signal Models In th... |

98 | An evaluation of multi-resolution storage for sensor networks
- Ganesan, Greenstein, et al.
- 2003
(Show Context)
Citation Context ...d on predictive coding [18–20], a distributed KLT [21], and distributed wavelet transforms [22, 23]. Three-dimensional wavelets have been proposed to exploit both inter- and intra-signal correlations =-=[24]-=-. Note, however, that any collaboration involves some amount of inter-sensor communication overhead. In the Slepian-Wolf framework for lossless distributed coding [13–17], the availability of correlat... |

96 | 1-bit compressive sensing
- Boufounos, Baraniuk
- 2008
(Show Context)
Citation Context ... to leverage, including variants of Basis Pursuit with Denoising [63, 69], robust iterative recovery algorithms [64], CS noise sensitivity analysis [25, 34], the Dantzig Selector [33], and one-bit CS =-=[70]-=-. Third, in some applications, the linear program associated with some DCS decoders (in JSM-1 and JSM-3) could prove too computationally intense. As we saw in JSM-2, efficient iterative and greedy alg... |

89 | The Distributed Karhunen-Loeve Transform
- Gastpar
- 2006
(Show Context)
Citation Context ...on point [13–17]. A number of distributed coding algorithms have been developed that involve collaboration amongst the sensors, including several based on predictive coding [18–20], a distributed KLT =-=[21]-=-, and distributed wavelet transforms [22, 23]. Three-dimensional wavelets have been proposed to exploit both inter- and intra-signal correlations [24]. Note, however, that any collaboration involves s... |

88 | Counting faces of randomly projected polytopes when the projection radically lowers dimension - Donoho, Tanner |

83 | Subspace pursuit for compressed sensing: Closing the gap between performance and complexity
- Dai, Milenkovich
(Show Context)
Citation Context ...ents with high probability, at the expense of slightly more measurements, [26, 43]. Algorithms inspired by OMP, such as regularized orthogonal matching pursuit [44], CoSaMP [45], and Subspace Pursuit =-=[46]-=- have been shown to attain similar guarantees to those of their optimization-based counterparts. In the following, we will exploit both Basis Pursuit and greedy algorithms for recovering jointly spars... |

83 | Atoms of all channels, unite! average case analysis of multichannel sparse recovery using greedy algorithms
- Gribonval, Rauhut, et al.
- 2008
(Show Context)
Citation Context ...k [47] and to the continuous-time setting [48]. Since the original submission of this paper, additional work has focused on the analysis and proposal of recovery algorithms for jointly sparse signals =-=[49, 50]-=-. 3 Joint Sparsity Signal Models In this section, we generalize the notion of a signal being sparse in some basis to the notion of an ensemble of signals being jointly sparse. 3.1 Notation We will use... |

80 | Distributed compressed sensing of jointly sparse signals
- Duarte, Sarvotham, et al.
- 2005
(Show Context)
Citation Context ...and AFOSR. Preliminary versions of this work have appeared at the 43rd Allerton Conference on Communication, Control, and Computing [1], the 39th Asilomar Conference on Signals, Systems and Computers =-=[2]-=-, and the 19th Conference on Neural Information Processing Systems [3]. Email: {drorb, wakin, duarte, shri, richb}@rice.edu; Web: dsp.rice.edu/csshave a sparse representation in terms of some basis, m... |

79 | Decentralized compression and predistribution via randomized gossiping - Rabbat, Haupt, et al. - 2006 |

64 |
Neighborliness of randomly projected simplices in high dimensions
- Donoho, Tanner
- 2005
(Show Context)
Citation Context ...early the probability increases with the number of measurements M = cK. Moreover, the curves become closer to a step function as N grows. In an illuminating series of recent papers, Donoho and Tanner =-=[32, 33]-=- have characterized the oversampling factor c(S) precisely. With appropriate oversampling, reconstruction via Basis Pursuit is also provably robust to measurement noise and quantization error [27]. In... |

61 | Distributed sparse random projections for refinable approximation - Wang, Garofalakis, et al. |

51 | Joint source-channel communication for distributed estimation in sensor networks - Bajwa, Haupt, et al. - 2007 |

50 |
Fast reconstruction of piecewise smooth signals from random projections
- Duarte, Wakin, et al.
- 2005
(Show Context)
Citation Context ...have also been developed to recover the signal x from the measurements y. Examples include the iterative Orthogonal Matching Pursuit (OMP) [30], matching pursuit (MP), and tree matching pursuit (TMP) =-=[35, 36]-=- algorithms. OMP, for example, iteratively selects the vectors from the holographic basis ΦΨ that contain most of the energy of the measurement vector y. The selection at each iteration is made based ... |

50 | Universal distributed sensing via random projections
- Duarte, Wakin, et al.
- 2006
(Show Context)
Citation Context ...oarser [39] (see also Section 7). Characterizing DCS in light of practical considerations such as rate-distortion tradeoffs, power consumption in sensor networks, etc., are topics of ongoing research =-=[40]-=-. 1.5 Paper organization Section 2 overviews the distributed source coding and single-signal CS theories and provides two new results on CS reconstruction. While readers may be familiar with some of t... |

48 | Measurements vs. bits: Compressed sensing meets information theory
- Sarvotham, Baron, et al.
- 2006
(Show Context)
Citation Context ...evant for measuring performance. For example, the measurements will typically be real numbers that must be quantized, which gradually degrades the recovery quality as the quantization becomes coarser =-=[33, 34]-=-. Characterizing DCS in light of practical considerations such as rate-distortion tradeoffs, power consumption in sensor networks, etc., are topics of future research [31, 32]. 1.4 Paper organization ... |

46 | Signal reconstruction using sparse tree representations
- La, Do
- 2005
(Show Context)
Citation Context ...have also been developed to recover the signal x from the measurements y. Examples include the iterative Orthogonal Matching Pursuit (OMP) [30], matching pursuit (MP), and tree matching pursuit (TMP) =-=[35, 36]-=- algorithms. OMP, for example, iteratively selects the vectors from the holographic basis ΦΨ that contain most of the energy of the measurement vector y. The selection at each iteration is made based ... |

43 | Universal lossless source coding with the Burrows Wheeler transform
- Effros, Visweswariah, et al.
- 2002
(Show Context)
Citation Context ...l symbols and thus can be viewed as the analogue of the Karhunen-Lòeve transform for sequences over finite alphabets. The BWT handles temporal correlation efficiently in single-source lossless coding =-=[41, 42]-=-. For distributed coding, the BWT could be proposed to remove temporal correlations by pre-processing the sequences prior to Slepian-Wolf coding. Unfortunately, the BWT is input-dependent, and hence t... |

39 | Simultaneous sparse approximation via greedy pursuit,” ICASSP
- Tropp, Gilbert, et al.
- 2005
(Show Context)
Citation Context ...on sparse supports: In this model, all signals are constructed from the same sparse set of basis vectors, but with different coefficient values. Examples of JSM-2 scenarios include MIMO communication =-=[34]-=- and audio signal arrays; the signals may be sparse in the Fourier domain, for example, yet multipath resulting from differing propagation paths causes different attenuations among the frequency compo... |

38 |
Distributed image compression for sensor networks using correspondence analysis and super-resolution
- Wagner, Nowak, et al.
- 2003
(Show Context)
Citation Context ...er work in this area will yield new JSMs suitable for other application scenarios. Applications that could benefit include multiple cameras taking digital photos of a common scene from various angles =-=[55]-=-. Additional extensions are discussed in Section 7. 4 Recovery Strategies for Sparse Common Component + Innovations (JSM-1) In Section 2.1.2, Theorem 1 specified an entire region of rate pairs where d... |

31 | A distributed wavelet compression algorithm for wireless multihop sensor networks using lifting
- Ciancio, Ortega
- 2005
(Show Context)
Citation Context ... coding algorithms have been developed that involve collaboration amongst the sensors, including several based on predictive coding [18–20], a distributed KLT [21], and distributed wavelet transforms =-=[22, 23]-=-. Three-dimensional wavelets have been proposed to exploit both inter- and intra-signal correlations [24]. Note, however, that any collaboration involves some amount of inter-sensor communication over... |

29 |
On the rate-distortion performance of compressed sensing
- Fletcher, Rangan, et al.
- 2007
(Show Context)
Citation Context ... ⎧ ⎫ ⎨ J∑ J∑ J∑ ⎬ |xj(1)|, |xj(2)|, ..., |xj(N)| ⎩ ⎭ . j=1 j=1 Second, (random) measurements are real numbers; quantization gradually degrades the recovery quality as the quantization becomes coarser =-=[34, 67, 68]-=-. Moreover, in many practical situations some amount of measurement noise will corrupt the {xj}, making them not exactly sparse in any basis. While characterizing these effects and the resulting rate-... |

28 | Recovery of jointly sparse signals from few random projections
- Wakin, Sarvotham, et al.
- 2005
(Show Context)
Citation Context ... Allerton Conference on Communication, Control, and Computing [1], the 39th Asilomar Conference on Signals, Systems and Computers [2], and the 19th Conference on Neural Information Processing Systems =-=[3]-=-. Email: {drorb, wakin, duarte, shri, richb}@rice.edu; Web: dsp.rice.edu/csshave a sparse representation in terms of some basis, meaning that a small number K of adaptively chosen transform coefficien... |

28 | LDPC codes for compression of multiterminal sources with hidden Markov correlation - García-Frías, Zhong - 2003 |

25 | An information-theoretic approach to distributed compressed sensing
- Baron, Duarte, et al.
- 2005
(Show Context)
Citation Context ...t many signals ∗ This work was supported by NSF-CCF, NSF-NeTS, ONR, and AFOSR. Preliminary versions of this work have appeared at the 43rd Allerton Conference on Communication, Control, and Computing =-=[1]-=-, the 39th Asilomar Conference on Signals, Systems and Computers [2], and the 19th Conference on Neural Information Processing Systems [3]. Email: {drorb, wakin, duarte, shri, richb}@rice.edu; Web: ds... |

22 | Distributed wavelet transform for irregular sensor network grids
- Wagner, Choi, et al.
- 2005
(Show Context)
Citation Context ... coding algorithms have been developed that involve collaboration amongst the sensors, including several based on predictive coding [18–20], a distributed KLT [21], and distributed wavelet transforms =-=[22, 23]-=-. Three-dimensional wavelets have been proposed to exploit both inter- and intra-signal correlations [24]. Note, however, that any collaboration involves some amount of inter-sensor communication over... |

19 |
A compressed sensing camera: New theory and an implementation using digital micromirrors
- Takhar, Bansal, et al.
- 2006
(Show Context)
Citation Context ...parse representation in some basis. Instead of sampling a K-sparse signal N times, only cK incoherent measurements suffice, where K can be orders of magnitude less than N. (For example, Takhar et al. =-=[37]-=- develop a camera that dispenses with the usual N-pixel CCD or CMOS imaging array by computing cK incoherent image projections optically using a digital micromirror device.) Therefore, a sensor can tr... |

19 |
and M.Vetterli, “Rate-distortion analysis of spike processes
- Weidmann
- 1999
(Show Context)
Citation Context ...ve sparsities KC ∼ Binomial(N,SC) and Kj ∼ Binomial(N,Sj). The parameters Sj and SC are sparsity rates controlling the random generation of each signal. Our model resembles the Gaussian spike process =-=[58]-=-, which is a limiting case of a Gaussian mixture model. Likelihood of sparsity reduction and overlap: This stochastic model can yield signal ensembles for which the corresponding generating matrices P... |

18 | Further results on spectrum blind sampling of 2D signals
- Venkataramani, Bresler
- 1998
(Show Context)
Citation Context ...taken to avoid ambiguity; the following theorem establishes that K + 1 random measurements will suffice. The proof appears in Appendix A; similar results were established by Venkataramani and Bresler =-=[50]-=-. Theorem 2 Let Ψ be an orthonormal basis for R N , and let 1 ≤ K < N. Then the following statements hold: 1. Let Φ be an M ×N measurement matrix with i.i.d. Gaussian entries with M ≥ 2K. Then with pr... |

18 |
On sensing capacity of sensor networks for the class of linear observation, fixed SNR models
- Aeron, Zhao, et al.
- 2007
(Show Context)
Citation Context ...tization becomes coarser [33, 34]. Characterizing DCS in light of practical considerations such as rate-distortion tradeoffs, power consumption in sensor networks, etc., are topics of future research =-=[31, 32]-=-. 1.4 Paper organization Section 2 overviews the single-signal CS theories and provides a new result on CS recovery. While some readers may be familiar with this material, we include it to make the pa... |

15 | Quantization of sparse representations
- Boufounos, Baraniuk
(Show Context)
Citation Context ... ⎧ ⎫ ⎨ J∑ J∑ J∑ ⎬ |xj(1)|, |xj(2)|, ..., |xj(N)| ⎩ ⎭ . j=1 j=1 Second, (random) measurements are real numbers; quantization gradually degrades the recovery quality as the quantization becomes coarser =-=[34, 67, 68]-=-. Moreover, in many practical situations some amount of measurement noise will corrupt the {xj}, making them not exactly sparse in any basis. While characterizing these effects and the resulting rate-... |

12 | An O(N) semipredictive universal encoder via the BWT
- Baron, Bresler
- 2004
(Show Context)
Citation Context ...l symbols and thus can be viewed as the analogue of the Karhunen-Lòeve transform for sequences over finite alphabets. The BWT handles temporal correlation efficiently in single-source lossless coding =-=[41, 42]-=-. For distributed coding, the BWT could be proposed to remove temporal correlations by pre-processing the sequences prior to Slepian-Wolf coding. Unfortunately, the BWT is input-dependent, and hence t... |

10 | Routing Explicit Side Information for Data Compression - Luo, Pottie - 2005 |

9 |
Near optimal approximation of arbitrary vectors from highly incomplete measurements, Inst. für Geometrie und Praktische Mathematik
- Cohen, Dahmen, et al.
- 2007
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Citation Context ...reviously selected columns. The algorithm has been proven to successfully recover the acquired signal from incoherent measurements with high probability, at the expense of slightly more measurements, =-=[26, 43]-=-. Algorithms inspired by OMP, such as regularized orthogonal matching pursuit [44], CoSaMP [45], and Subspace Pursuit [46] have been shown to attain similar guarantees to those of their optimization-b... |

6 |
Fundamental limits on sensing capacity for sensor networks and compressed sensing.” arXiv:0804.3439v1 [cs.IT
- Aeron, Zhao, et al.
- 2009
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Citation Context ...tization becomes coarser [33, 34]. Characterizing DCS in light of practical considerations such as rate-distortion tradeoffs, power consumption in sensor networks, etc., are topics of future research =-=[31, 32]-=-. 1.4 Paper organization Section 2 overviews the single-signal CS theories and provides a new result on CS recovery. While some readers may be familiar with this material, we include it to make the pa... |

4 | Theoretic performance limits for jointly sparse signals via graphical models
- Duarte, Sarvotham, et al.
- 2008
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Citation Context ...omputing [1], the Asilomar Conference on Signals, Systems and Computers [2], the Conference on Neural Information Processing Systems [3], and the Workshop on Sensor, Signal and Information Processing =-=[4]-=-. E-mail: drorb@ee.technion.ac.il, {duarte, shri, richb}@rice.edu, mwakin@mines.edu; Web: dsp.rice.edu/csCurrent state-of-the-art compression algorithms employ a decorrelating transform such as an ex... |

4 | Distributed compressed sensing: Sparsity models and reconstruction algorithms using annihilating filter
- Hormati, Vetterli
- 2008
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Citation Context ...at are agnostic to the spatial sampling structure and that exploit both inter- and intra-signal correlations. Recent work has adapted DCS to the finite rate of innovation signal acquisition framework =-=[47]-=- and to the continuous-time setting [48]. Since the original submission of this paper, additional work has focused on the analysis and proposal of recovery algorithms for jointly sparse signals [49, 5... |

3 |
A remark on simultaneous sparse approximation
- Temlyakov
(Show Context)
Citation Context ...rocessing algorithms. Another useful application for JSM-2 is MIMO communication [34]. Similar signal models have been considered by different authors in the area of simultaneous sparse approximation =-=[34, 52, 53]-=-. In this setting, a collection of sparse signals share the same expansion vectors from a redundant dictionary. The sparse approximation can be recovered via greedy algorithms such as Simultaneous Ort... |

3 |
Analysis of the DCS one-stage greedy algoritm for common sparse supports
- Sarvotham, Wakin, et al.
- 2005
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Citation Context ...s per Signal, M Figure 9: Reconstruction using OSGA for JSM-2. Approximate formula (dashed lines) for the probability of error in recovering the support set Ω in JSM-2 using OSGA given J, N, K, and M =-=[56]-=- compared against simulation results (solid) for fixed N = 50, K = 5 and varying number of measurements M and number of signals J = 5, J = 20, and J = 100. Theorem 9 Assume that the nonzero coefficien... |

2 | Universal coding for correlated sources with memory
- Uyematsu
- 2001
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Citation Context ... of the data to remove intra-signal correlations combined with Slepian-Wolf coding for the inter-signal correlations appear to have limited applicability. Finally, although a recent paper by Uyematsu =-=[26]-=- provides compression of spatially correlated sources with memory, the solution is specific to lossless distributed compression and cannot be readily extended to lossy compression setups. We conclude ... |

1 | Slepian-Wolf coding of binary finite memory sources using Burrows Wheeler transform - Chen, Ji, et al. - 2009 |