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## Sensing, Compression and Recovery for Wireless Sensor Networks: Monitoring Framework Design

### Citations

12434 | Elements of Information Theory. - Cover, Thomas - 2006 |

4324 |
Estimating the dimension of a model.
- Schwarz
- 1978
(Show Context)
Citation Context ...idence involves the computation of analytically intractable integrals. For this reason, we rank the different models according to a widely used approximation, the Bayesian Information Criterion (BIC) =-=[29]-=-, that we define as: BIC(Mi) def = ln [p(D|θMAP ,Mi)p(θMAP |Mi)]− `i 2 ln(T ) , (11) where θMAP is defined in (10), `i is the number of free parameters of model Mi and T is the cardinality of the obse... |

3625 | Compressed sensing,”
- Donoho
- 2006
(Show Context)
Citation Context ...al source coding (e.g., see [7]–[9]) in a distributed fashion. New methods for distributed sensing and compression have been developed, instead, based on the recent theory of Compressive Sensing (CS) =-=[10]-=-–[12]. CS is a novel data compression technique that exploits the inherent structure of some input data set to compress it by means of quasi-random matrices; recovery of the original data is achieved ... |

3482 |
The elements of statistical learning,
- Hastie, Tibshirani, et al.
- 2009
(Show Context)
Citation Context ...ince the number of equations L is smaller than the number of variables N . It may also be ill-conditioned, i.e., a small variation of the output y(k) can produce a large variation of the input signal =-=[17]-=-, [18]. However, if s(k) is sparse, it has been shown that (4) can be inverted with high probability through the use of specialized optimization techniques [3], [19]. These allow to retrieve s(k), fro... |

2632 | Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,”
- Candes, Romberg, et al.
- 2004
(Show Context)
Citation Context ...urce coding (e.g., see [7]–[9]) in a distributed fashion. New methods for distributed sensing and compression have been developed, instead, based on the recent theory of Compressive Sensing (CS) [10]–=-=[12]-=-. CS is a novel data compression technique that exploits the inherent structure of some input data set to compress it by means of quasi-random matrices; recovery of the original data is achieved solvi... |

1513 | Near optimal signal recovery from random projections: Universal encoding strategies?”
- Candes, Tao
- 2006
(Show Context)
Citation Context ... can invert Eq. (4) solving a convex optimization problem, e.g., see [25]. The idea of iteratively exploiting PCA to compute the sparsifying matrix Ψ for CS is the key point of CS-PCA. In standard CS =-=[11]-=-, Ψ is assumed to be given and fixed with time, but this is not the case for a realistic WSN scenario, where the statistical characteristics of x(k), the signal of interest, can vary with time. To cop... |

1262 |
Noiseless coding of correlated information sources,”
- Slepian, Wolf
- 1973
(Show Context)
Citation Context ...ources which are correlated both temporally and spatially. Subsequent work such as [2]–[6] proposed algorithms that involve collaboration among sensors to implement classical source coding (e.g., see =-=[7]-=-–[9]) in a distributed fashion. New methods for distributed sensing and compression have been developed, instead, based on the recent theory of Compressive Sensing (CS) [10]–[12]. CS is a novel data c... |

915 |
Probabilistic Graphical Models: Principles and Techniques,
- Koller, Friedman
- 2009
(Show Context)
Citation Context ..., depicting the probabilistic relations among all the variables involved in the compression, transmission and recovery process through a Bayesian Network (BN). A BN is a probabilistic graphical model =-=[10]-=-, a very useful tool to graphically capture the probabilistic relations among a set of random variables and to study the conditional probabilities within this set. This tool has been used for networki... |

766 |
Matrix Analysis and Applied Linear Algebra. Philadelphia: Society for Industrial and Applied Mathematics (SIAM),
- Meyer
- 2000
(Show Context)
Citation Context ...+U(k)M s (k) , (10) where, in general, V(k) can be any [N ×M ] matrix of orthonormal columns (obtained at time k from the set {x(k−K)−x(k), . . . ,x(k−1)−x(k)}, e.g., through the Gram-Schmidt process =-=[28]-=-), with M ≤ N ; here we set V(k) = U(k)M because given M ≤ N , the best way to represent with M components each element out of a set of N−dimensional elements is through PCA. In order to show that PCA... |

728 | Bayesian interpolation.
- MacKay
- 1992
(Show Context)
Citation Context ... in Eq. (5) and the r.v. xj is an element of vector x. A statistical model for each si can be determined through the Bayesian estimation procedure detailed below. Similarly to the approach adopted in =-=[28]-=-, we rely upon two levels of inference. First level of inference. Given a set of competitive models {M1, · · · ,MN} for the observed phenomenon, each of them depending on the parameter vector θ, we fi... |

407 | Distributed source coding using syndromes (DISCUS): design and construction,” - Pradhan, Ramchandran - 1999 |

330 | Bayesian compressive sensing,”
- Ji, Xue, et al.
- 2008
(Show Context)
Citation Context ...and compression of digital images, which show high spatial correlation. In the very recent literature, the Bayesian approach has been used to develop efficient and auto-tunable algorithms for CS, see =-=[4]-=-. However, previous work addressing CS from a Bayesian perspective mainly focused on proving fundamental results and on understanding its usefulness in the image processing field. In particular, in [5... |

239 | Signal reconstruction from noisy random projections,”
- Haupt, Nowak
- 2006
(Show Context)
Citation Context ...hors model the components of the CS problem using a Bayesian framework to recover synthetic 1-D sparse signals and simple images with high spatial correlation. Since the pioneering work of Nowak [7], =-=[8]-=-, there has been a growing interest in this technique also in the networking community. Specifically, the great interest around the use of CS in Wireless Sensor Networks (WSNs) comes from the fact tha... |

224 | Distributed source coding for sensor networks.
- Xiong, Liveris, et al.
- 2004
(Show Context)
Citation Context ...es which are correlated both temporally and spatially. Subsequent work such as [2]–[6] proposed algorithms that involve collaboration among sensors to implement classical source coding (e.g., see [7]–=-=[9]-=-) in a distributed fashion. New methods for distributed sensing and compression have been developed, instead, based on the recent theory of Compressive Sensing (CS) [10]–[12]. CS is a novel data compr... |

143 |
The use and interpretation of principal component analysis in applied research.
- Rao
- 1964
(Show Context)
Citation Context ...construction error and acts on the recovery process in order to keep this error bounded. Also, we study the performance achievable by means of a joint use of CS and Principal Component Analysis (PCA) =-=[20]-=- as an interpolation technique. This investigation is based on the results presented in the companion paper [21], where we explain the sparse signal modeling underneath our framework and show that the... |

111 | A fast approach for overcomplete sparse decomposition based on smoothed
- Mohimani, Jutten
- 2009
(Show Context)
Citation Context ...hanism of SCoRe1 we can use CS and PCA in combination. The original signal x(k) is approximated as follows: 1) find a good estimate5 of s(k), namely ŝ(k), e.g., using the algorithms in [12], [25] or =-=[26]-=-, and 2) apply the following calculation: x̂(k) = x(k) +U(k)ŝ(k) . (6) A. SCoRe1 Framework Validation In order to illustrate the choices made in the design of SCoRe1, we consider two simple strategie... |

91 | The distributed KarhunenLoève transform,”
- Gastpar, Dragotti, et al.
- 2006
(Show Context)
Citation Context ...d as key ingredients for joint data gathering and compression. In fact, WSN applications often involve multiple sources which are correlated both temporally and spatially. Subsequent work such as [2]–=-=[6]-=- proposed algorithms that involve collaboration among sensors to implement classical source coding (e.g., see [7]–[9]) in a distributed fashion. New methods for distributed sensing and compression hav... |

80 | Decentralized compression and predistribution via randomized gossiping,” in
- Rabbat, Haupt, et al.
- 2006
(Show Context)
Citation Context ...he energy efficient estimation of sensed data in a WSN. In this approach, data packets are directly transmitted by each node to the Data Collection Point (DCP), requiring synchronization among nodes. =-=[14]-=- proposes an interesting application involving CS for fault detection, using a pre-distribution phase (via simple gossiping algorithms), which is however very expensive in terms of number of transmiss... |

70 |
Linear inverses and ill-posed problems, in:
- Bertero
- 1989
(Show Context)
Citation Context ...he number of equations L is smaller than the number of variables N . It may also be ill-conditioned, i.e., a small variation of the output y(k) can produce a large variation of the input signal [17], =-=[18]-=-. However, if s(k) is sparse, it has been shown that (4) can be inverted with high probability through the use of specialized optimization techniques [3], [19]. These allow to retrieve s(k), from whic... |

68 | Bayesian compressive sensing using laplace priors,”
- Babacan, Molina, et al.
- 2010
(Show Context)
Citation Context ...ayesian model is considered to utilize CS for the reconstruction of sparse images when the observations are obtained from linear transformations and corrupted by additive and white Gaussian noise. In =-=[6]-=-, the authors model the components of the CS problem using a Bayesian framework to recover synthetic 1-D sparse signals and simple images with high spatial correlation. Since the pioneering work of No... |

53 | Joint source–channel communication for distributed estimation in sensor networks,”
- Bajwa, Haupt, et al.
- 2007
(Show Context)
Citation Context ...s of quasi-random matrices; recovery of the original data is achieved solving a convex optimization problem, i.e., an L1 norm minimization. An early application of CS to wireless sensor networking is =-=[13]-=-, where CS is used in a distributed communication scheme for the energy efficient estimation of sensed data in a WSN. In this approach, data packets are directly transmitted by each node to the Data C... |

42 | On the interplay between routing and signal representation for compressive sensing in wireless sensor networks,”
- Quer, Masiero, et al.
- 2009
(Show Context)
Citation Context ...ation of the sensor readings. The spatial correlation is then exploited at the sink by means of suitable decoders through a joint sparsity model that well characterizes different types of signals. In =-=[18]-=- the network topology and the routing used to transport the random projections of the data to the sink have been taken into account to evaluate the possible benefits of CS in realistic multi-hop WSNs.... |

42 |
Maximum entropy and Bayesian methods
- Skilling
- 1989
(Show Context)
Citation Context ...conjunction with different interpolation techniques in the presence of real world signals. The present work is also related to the literature on signal recovery and on Bayesian theory, e.g., see [22]–=-=[24]-=-. Further, we stress that SCoRe1 is proposed for WSNs, but it can be readily applied to other types of network infrastructures that require the approximation of large and distributed datasets with spa... |

35 | Distributed signal processing algorithms for the sensor broadcast problem
- Servetto
- 2003
(Show Context)
Citation Context ...posed as key ingredients for joint data gathering and compression. In fact, WSN applications often involve multiple sources which are correlated both temporally and spatially. Subsequent work such as =-=[2]-=-–[6] proposed algorithms that involve collaboration among sensors to implement classical source coding (e.g., see [7]–[9]) in a distributed fashion. New methods for distributed sensing and compression... |

30 | Hierarchical bayesian sparse image reconstruction with application to MRFM
- Dobigeon, Hero, et al.
(Show Context)
Citation Context ...4]. However, previous work addressing CS from a Bayesian perspective mainly focused on proving fundamental results and on understanding its usefulness in the image processing field. In particular, in =-=[5]-=- a hierarchical Bayesian model is considered to utilize CS for the reconstruction of sparse images when the observations are obtained from linear transformations and corrupted by additive and white Ga... |

25 |
Bayesian and Related Methods in Image Reconstruction from Incomplete data,” in Image Recovery: Theory and Application,
- Hanson
- 1987
(Show Context)
Citation Context ...le mean return the best approximation of the original vector, in accordance to Eq. (10). To solve Problem 3.1 exploiting the model in Eq. (10) we can simply use the Ordinary Least Square (OLS) method =-=[22]-=-, thus we refer to this recovery solution as Deterministic Ordinary Least Square. From y(k) = Φ(k)x(k) and the assumption that Eq. (10) holds, we can write y(k) = Φ(k)(x(k) +U (k) M s (k)) . (13) The ... |

22 |
Servetto: On the Interdependence of Routing and
- Scaglione, D
- 2002
(Show Context)
Citation Context ...ess Sensor Networks (WSNs) has been widely researched in the past few years. One of the first studies addressing the problem of efficiently gathering correlated data from a wide network deployment is =-=[1]-=-, which highlights the interdependence among the bandwidth, the decoding delay and the routing strategy employed. Under certain assumptions of regularity of the observed process, the authors claim the... |

17 | Efficient measurement generation and pervasive sparsity for compressive data gathering,”
- Luo, Wu, et al.
- 2010
(Show Context)
Citation Context ...ount to evaluate the possible benefits of CS in realistic multi-hop WSNs. In addition, different transformations have been evaluated in order to meet the sparsity requirements of CS. In a recent work =-=[19]-=-, the authors proposed an interesting in-network aggregation technique and exploited CS to reconstruct the data at the sink. Differently to our approach, the aggregation technique depends on the netwo... |

14 | Compressed network monitoring,”
- Coates, Pointurier, et al.
- 2007
(Show Context)
Citation Context ...e topologies are exploited for data gathering and routing, and the Wavelet transformation is used for data compression. An interesting application for network monitoring exploiting CS is presented in =-=[16]-=-, where the aim is to efficiently monitor communication metrics, such as loss or delay, over a set of end-to-end network paths by observing only a subset of them. In [17] an approach to distributed co... |

13 | Data Acquisition Through Joint Compressive Sensing and Principal Component Analysis,"
- Masiero
- 2009
(Show Context)
Citation Context ...he most appropriate sampling, compression and recovery techniques to minimize the number of transmitting nodes while keeping a certain level of reconstruction accuracy, as detailed in Section VI. 3In =-=[20]-=- we presented a practical scheme that does not need this assumption in order to work. 4In this paper we refer to a good estimate of s(k) as ŝ(k) such that ‖s(k) − ŝ(k)‖2 ≤ . Note that by keeping ... |

11 | Routing explicit side information for data compression in wireless sensor networks - Luo, Pottie - 2005 |

11 |
Entropy and the central limit theorem,” The Annals of Probability
- Barron
- 1986
(Show Context)
Citation Context ...nals, see Fig. 9, signal S2. In fact the uncertainty on the training set makes the Gaussian prior for s(k) more effective than the Laplacian one, in accordance to the central limit theorem (e.g., see =-=[31]-=-). Nevertheless, both POLS and CS-PCA remain valid solutions for a monitoring application framework, since the performance loss from the ideal case, which assumes perfect knowledge of TK , to the one ... |

11 |
Compressed sensing for networked data: a different approach to decentralized compression,”
- Haupt, Bajwa, et al.
- 2008
(Show Context)
Citation Context ...e authors model the components of the CS problem using a Bayesian framework to recover synthetic 1-D sparse signals and simple images with high spatial correlation. Since the pioneering work of Nowak =-=[7]-=-, [8], there has been a growing interest in this technique also in the networking community. Specifically, the great interest around the use of CS in Wireless Sensor Networks (WSNs) comes from the fac... |

10 |
Biharmonic Spline Interpolation of GEOS-3
- Sandwell
- 1987
(Show Context)
Citation Context ...r function of the d−dimensional coordinate c, φ(c) (e.g., the Green function) that satisfies regularity conditions (e.g., smoothness) inferred by “typical” realizations of the signal of interest x(k) =-=[27]-=-. Thus, we can write each element i of x(k) as x (k) i (c (i)) ' L∑ j=1 αjφ(c (i) − c(j)) , (8) where the function φ(·) is used as a sort of basis function for x(k) and αj is the weight associated wit... |

8 | Novel distributed wavelet transforms and routing algorithms for efficient data gathering in sensor webs
- Shen, Lee, et al.
(Show Context)
Citation Context ...ses an interesting application involving CS for fault detection, using a pre-distribution phase (via simple gossiping algorithms), which is however very expensive in terms of number of transmissions. =-=[15]-=- also addresses the problem of gathering data in distributed WSNs through multi-hop routing: tree topologies are exploited for data gathering and routing, and the Wavelet transformation is used for da... |

6 |
SensorScope WSN,” Last time accessed
- LUCE
- 2009
(Show Context)
Citation Context ...ploit any prior knowledge on the statistics of the signal to recover. Finally, in Fig. 10 we show similar performance curves using the signals gathered from the EPFL WSN deployment LUCE, see [21] and =-=[32]-=-. The signals considered in this figure are of the class S1, i.e., temperature and humidity. Also in this case, the performance are similar to Fig. 8 and all the above observations remain valid. This ... |

6 |
Using Bayesian Networks for Cognitive
- Quer, Meenakshisundaram, et al.
- 2010
(Show Context)
Citation Context ... variables and to study the conditional probabilities within this set. This tool has been used for networking applications in recent papers on the optimization of single-hop [11] as well as multi-hop =-=[12]-=- Wireless Local Area Networks (WLAN). In order to substantiate our framework, we consider different WSN testbeds, whose data is available on-line. We analyze the statistics of the principal components... |

5 | WSN-Control: Signal Reconstruction through Compressive Sensing
- Quer, Zordan, et al.
- 2010
(Show Context)
Citation Context ...g matrix U(k) are derived from the samples of the recorded training set (i.e., mean and covariance matrix), and the CS recovery problem is solved via a convex optimization problem, e.g., see [30] and =-=[31]-=-. Figs. 8–9 show the quality of the monitored signal reconstruction (at the application server) vs the transmission probability ptx. The results are obtained implementing the simple above mechanism co... |

4 |
Cognitive Network Inference through Bayesian Network Analysis
- Quer, Meenakshisundaram, et al.
- 2010
(Show Context)
Citation Context ...ions among a set of random variables and to study the conditional probabilities within this set. This tool has been used for networking applications in recent papers on the optimization of single-hop =-=[11]-=- as well as multi-hop [12] Wireless Local Area Networks (WLAN). In order to substantiate our framework, we consider different WSN testbeds, whose data is available on-line. We analyze the statistics o... |

3 |
The Use and Interpretation of Principal Component Analysis
- Gull
- 1988
(Show Context)
Citation Context ...ing a Bayesian model to approximate the statistical distribution of the principal components. An overview on the use of Bayesian theory to define a general framework for data modeling can be found in =-=[13]-=-, [14]. Hence, we provide empirical evidence of the effectiveness of CS in actual WSNs, showing that the principal components of real signals are well approximated by a Laplacian distribution. Moreove... |

3 |
NESTA: a fast and accurate first order method for sparse recovery.” Submitted for publication. [Online]. Available: http://www-stat.stanford.edu/∼candes/papers/NESTA.pdf
- Bercker, Bobin, et al.
(Show Context)
Citation Context ...on paper [21] we verified that, when Ψ is obtained through PCA, s(k) is a sparse vector for many signals of interest; therefore, we can invert Eq. (4) solving a convex optimization problem, e.g., see =-=[25]-=-. The idea of iteratively exploiting PCA to compute the sparsifying matrix Ψ for CS is the key point of CS-PCA. In standard CS [11], Ψ is assumed to be given and fixed with time, but this is not the c... |

3 |
On a theorem of Weil concerning eigenvalues of linear transformation I
- Fan
- 1949
(Show Context)
Citation Context ...rovides the best fit to all the elements in T (k)K , and therefore for all the vectors that lie in span 〈 T (k)K 〉 , in terms of minimum Euclidean distance. The key point of PCA is the Ky Fan theorem =-=[29]-=-, here reported to better illustrate the considered deterministic approach. Theorem 3.1 (Ky Fan Theorem): Let Σ ∈ RN×N be a symmetric matrix, let λ1 ≥ · · · ≥ λN be its eigenvalues and u1, . . . ,uN t... |

3 |
The Design, Deployment, and Analysis of SignetLab: A
- Crepaldi, Friso, et al.
- 2007
(Show Context)
Citation Context ...ive experimental network scenarios follows. T1 WSN testbed of the Department of Information Engineering (DEI) at the University of Padova, collecting data from 68 TmoteSky wireless sensor nodes [22], =-=[23]-=-. The node hardware features an IEEE 802.15.4 Chipcon wireless transceiver working at 2.4 GHz and allowing a maximum data rate of 250 Kbps. These sensors have a TI MSP430 micro-controller with 10 Kbyt... |

3 |
Sense&Sensitivity: A Large-Scale Experimental Study of Reactive Gradient Routing
- Watteyne, Barthel, et al.
- 2010
(Show Context)
Citation Context ...e transmitting interface is reconfigurable by the user and by default it operates in 802.11b/g ad hoc mode at 2.4 GHz. Nowadays this WSN deployment counts about twenty nodes; T5 The Sense&Sensitivity =-=[27]-=- testbed is a WSN of 86 nodes, which embed Texas Instrument Inc. technology: a MSP430 micro-controller and a CC1100 radio chip operating in the ISM band (from 315 to 915 MHz). Signals. From the above ... |

2 |
Universal Distributed Sensing via Random
- Duarte, Wakin, et al.
- 2006
(Show Context)
Citation Context ...exploiting CS is presented in [16], where the aim is to efficiently monitor communication metrics, such as loss or delay, over a set of end-to-end network paths by observing only a subset of them. In =-=[17]-=- an approach to distributed coding and compression in sensor networks based on CS is presented. The authors advocate the need to exploit the data correlation both temporally and spatially. The project... |

2 |
time accessed
- “CitySense
- 2011
(Show Context)
Citation Context ...t. Bernard pass at 2400 m, between Switzerland and Italy. See point T2 for a brief description of the related hardware; T4 CitySense WSN testbed, developed by Harvard University and BBN Technologies, =-=[26]-=-. CitySense is an urban scale deployment that will consist of 100 wireless sensor nodes equipped with an ALIX 2d2 single-board computer. The transmitting interface is reconfigurable by the user and by... |

1 | Massively Distributed Compression of Sensor Images - Lena - 2003 |

1 |
Sampling and Recovery with Compressive Sensing
- Masiero, Quer, et al.
- 2011
(Show Context)
Citation Context ...ormance achievable by means of a joint use of CS and Principal Component Analysis (PCA) [20] as an interpolation technique. This investigation is based on the results presented in the companion paper =-=[21]-=-, where we explain the sparse signal modeling underneath our framework and show that the Laplacian distribution provides an accurate representation of the statistics of the data measured from real WSN... |

1 |
SCoRe1: Sensing Compression and Recovery through Online Estimation for Wireless Sensor Networks,” Submitted to
- Quer, Masiero, et al.
- 2011
(Show Context)
Citation Context ...e integration of the proposed mathematical framework into an actual Data Collection and Recovery technique for WSN signals, with an extensive performance analysis, is presented in the companion paper =-=[15]-=-, where we compare this technique with other data collection methods that exploit the same information learned by PCA, as well as with standard data recovery schemes. 3The rest of the paper is structu... |