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## Field Reconstruction in Sensor Networks with Coverage Holes and Packet Losses

### Citations

400 | Robust distributed network localization with noisy range measurements
- Moore, Leonard, et al.
- 2004
(Show Context)
Citation Context ...ints, however, are known to the sink node, because (i) either sensors are located at pre-defined positions or their position can be estimated September 6, 2010 DRAFT 5through a localization technique =-=[25]-=-, and (ii) the sampling time is either periodic or included in the information sent to the sink. Now, let s = [s(x1), . . . , s(xm)]T be the values of the samples at [x1, . . . ,xm], respectively. Fol... |

362 |
Distributions of eigenvalues for some sets of random matrices
- Marchenko, Pastur
- 1967
(Show Context)
Citation Context ...igenvalues behavior, still for the case of non-folded Vandermonde matrices, can be found in [23]. Moreover, in [9] it has been shown that the LSD of VVH converges to the Marčenko-Pastur distribution =-=[24]-=- when V is d-fold Vandermonde with uniformly distributed phases and d→∞. Note that, with respect to previous studies on Vandermonde matrices with entries that are randomly September 6, 2010 DRAFT 4dis... |

121 | Spatio-temporal correlation: theory and applications for wireless sensor networks. - Vuran, Akan, et al. - 2004 |

91 |
Nonuniform Sampling. Theory and Practice.
- Marvasti
- 2001
(Show Context)
Citation Context ...y measurement. (iv) The sensors may be loosely synchronized, hence sense the field at different time instants. Clearly, sampling irregularities may result in a degradation of the reconstructed signal =-=[4]-=-. The work in [5] investigates this issue in the context of sensor networks. Other interesting studies can be found in [6] and [7], just to name a few, which address the perturbations of regular sampl... |

90 | Backcasting: adaptive sampling for sensor networks.
- Willett, Martin, et al.
- 2004
(Show Context)
Citation Context ...h the sample has been collected by the sensor, it will not be delivered to the central controller. (iii) The sensors may enter a low-power operational state (sleep mode), in order to save energy [2], =-=[3]-=-. While in sleep mode, the nodes neither perform sensing operations nor transmit/receive any measurement. (iv) The sensors may be loosely synchronized, hence sense the field at different time instants... |

79 | Image Reconstruction and Enhanced Resolution Imaging from Irregular Samples,”
- Early, Long
- 2001
(Show Context)
Citation Context ...rregularities may result in a degradation of the reconstructed signal [4]. The work in [5] investigates this issue in the context of sensor networks. Other interesting studies can be found in [6] and =-=[7]-=-, just to name a few, which address the perturbations of regular sampling in shift-invariant spaces [6] and the reconstruction of irregularly sampled images in presence of measure noise [7]. In this w... |

75 | Coping with irregular spatio-temporal sampling in sensor networks.
- Ganesan, Ratnasamy, et al.
- 2004
(Show Context)
Citation Context ...v) The sensors may be loosely synchronized, hence sense the field at different time instants. Clearly, sampling irregularities may result in a degradation of the reconstructed signal [4]. The work in =-=[5]-=- investigates this issue in the context of sensor networks. Other interesting studies can be found in [6] and [7], just to name a few, which address the perturbations of regular sampling in shift-inva... |

61 | Packetostatics: deployment of massively dense sensor networks as an electrostatics problem
- Toumpis, Tassiulas
(Show Context)
Citation Context ...ply our results to the study of network scenarios of practical interest, such as sensor sensor deployments with coverage holes, communication in presence of a fading channel, massively dense networks =-=[13]-=-, [14], and networks using contention-based channel access techniques [15]. The rest of the paper is organized as follows. Section II reviews previous work, while Section III describes the system mode... |

29 | On the optimal density for real-time data gathering of spatio-temporal processes in sensor networks
- Cristescu, Vetterli
- 2005
(Show Context)
Citation Context ... . ,m. September 6, 2010 DRAFT 3are applied to different practical scenarios in Section VI. Finally, Section VII concludes the paper. II. RELATED WORK In the context of sensor networks, several works =-=[16]-=-–[19] have studied the field reconstruction at the sink node in presence of spatial and temporal correlation among sensor measurements. In particular, in [19] the observed field is a discrete vector o... |

29 | Reconstruction of irregularly sampled discrete-time bandlimited signals with unknown sampling locations
- Marziliano, Vetterli
- 2000
(Show Context)
Citation Context ...mples so as to reconstruct the field with the required accuracy. The problem of reconstructing a bandlimited field from a set of irregular samples at unknown locations, instead, has been addressed in =-=[21]-=-. There, the field is oversampled by irregularly spaced sensors; sensor positions are unknown but always equal to an integer multiple of the sampling interval. Different solution methods are proposed,... |

27 |
Sensing Capacity for Discrete Sensor Network Applications
- Rachlin, Negi, et al.
- 2005
(Show Context)
Citation Context .... September 6, 2010 DRAFT 3are applied to different practical scenarios in Section VI. Finally, Section VII concludes the paper. II. RELATED WORK In the context of sensor networks, several works [16]–=-=[19]-=- have studied the field reconstruction at the sink node in presence of spatial and temporal correlation among sensor measurements. In particular, in [19] the observed field is a discrete vector of tar... |

22 |
Smart Sensors to Network the World,” Scientific American
- Culler, Mulder
- 2004
(Show Context)
Citation Context ...lar sampling are multifold. (i) The sensors may be irregularly deployed in the geographical region of interest, either due to the adopted deployment procedure (e.g., sensors thrown out of an airplane =-=[1]-=-), or due to the presence of terrain asperities and obstacles. (ii) The transmission of the measurements from the sensors to the central controller may fail due to bad channel propagation conditions (... |

22 | Random matrices and wireless communications, Foundations and trends - Tulino, Verdú - 2004 |

22 |
R.: Making everyday life easier using dense sensor networks
- Conner, Krishnamurthy, et al.
- 2001
(Show Context)
Citation Context ...r results to the study of network scenarios of practical interest, such as sensor sensor deployments with coverage holes, communication in presence of a fading channel, massively dense networks [13], =-=[14]-=-, and networks using contention-based channel access techniques [15]. The rest of the paper is organized as follows. Section II reviews previous work, while Section III describes the system model unde... |

19 | An energy conservation method for wireless sensor networks employing a blue noise spatial sampling technique
- Perillo, Ignjatovic, et al.
- 2004
(Show Context)
Citation Context ...though the sample has been collected by the sensor, it will not be delivered to the central controller. (iii) The sensors may enter a low-power operational state (sleep mode), in order to save energy =-=[2]-=-, [3]. While in sleep mode, the nodes neither perform sensing operations nor transmit/receive any measurement. (iv) The sensors may be loosely synchronized, hence sense the field at different time ins... |

16 |
Enhanced Markov Chain Model and Throughput Analysis of the Slotted CSMA/CA for IEEE 802.15.4 Under Unsaturated Traffic Conditions. Vehicular Technology,
- Jung, Hwang, et al.
- 2009
(Show Context)
Citation Context ...hat packets, whose transmission fails, are discarded. In order to derive the probability that a packet transmission fails within a cluster due to collision, we use the Markov chain model presented in =-=[28]-=-. We denote by mi,h the average number of sensors belonging to the generic cluster at the h-th layer of the hierarchical architecture, in area Ai (i = 1, . . . , L and h = 1, . . . ,H). Similarly, we ... |

12 | Reconstruction of multidimensional signals from irregular noisy samples
- Nordio, Chiasserini, et al.
(Show Context)
Citation Context ...nimizes the MSE (i.e., the LMMSE filter) [8]–[10]. The matrix representing the sampling system, in the following denoted by V, results to be a d-fold Vandermonde matrix1. By drawing on the results in =-=[9]-=-, [11], we derive both the moments and an expression of the limiting spectral distribution (LSD) of VVH, as the size of V goes to infinity and its aspect ratio has a finite limit bounded away from zer... |

11 | Performance of linear field reconstruction techniques with noise and uncertain sensor locations
- Nordio, Chiasserini, et al.
- 2008
(Show Context)
Citation Context ...rformance metric the mean square error (MSE) on the reconstructed field. As a reconstruction technique, we use linear filtering and we adopt the filter that minimizes the MSE (i.e., the LMMSE filter) =-=[8]-=-–[10]. The matrix representing the sampling system, in the following denoted by V, results to be a d-fold Vandermonde matrix1. By drawing on the results in [9], [11], we derive both the moments and an... |

8 | Impact of data retrieval pattern on homogeneous signal field reconstruction in dense sensor networks
- Dong, Tong, et al.
- 2006
(Show Context)
Citation Context ... maximum value of the ratio of the target positions to the number of sensors, is studied as a function of the noise, the sensing function and the sensor connectivity level. The paper by Dong and Tong =-=[20]-=- considers a dense sensor network where a MAC protocol is responsible to collect samples from network nodes. The work analyzes the impact of deterministic and random data collection strategies on the ... |

8 |
Eigenvalue results for large scale random vandermonde matrices with unit complex entries
- Whiting
(Show Context)
Citation Context ...es, for the non-folded case (i.e., d = 1), has recently appeared in [22]; further insights on the extremal eigenvalues behavior, still for the case of non-folded Vandermonde matrices, can be found in =-=[23]-=-. Moreover, in [9] it has been shown that the LSD of VVH converges to the Marčenko-Pastur distribution [24] when V is d-fold Vandermonde with uniformly distributed phases and d→∞. Note that, with res... |

8 |
S.V.: Cluster-based Congestion Control for Sensor Networks
- Karenos, Kalogeraki, et al.
(Show Context)
Citation Context ...formly deployed over a square region. We also identify L areas, Ai i = 1, . . . , L, each corresponding to a different value of the offered traffic load. As often assumed in the literature (see e.g., =-=[26]-=-, [27]) and widely applied in the practice, the network is divided into clusters and a hierarchy of clusters is created. More specifically, at the first hierarchical layer, layer 1, the sensors are gr... |

7 |
Perturbation of regular sampling in shift-invariant spaces for frames
- Zhao, Zhao, et al.
- 2006
(Show Context)
Citation Context ...mpling irregularities may result in a degradation of the reconstructed signal [4]. The work in [5] investigates this issue in the context of sensor networks. Other interesting studies can be found in =-=[6]-=- and [7], just to name a few, which address the perturbations of regular sampling in shift-invariant spaces [6] and the reconstruction of irregularly sampled images in presence of measure noise [7]. I... |

5 | Sensor activation and scheduling for field detection in large sensor arrays - Sung, Tong, et al. - 2005 |

3 | Tools for convolution operations arising from Vandermonde matrices
- Ryan
- 2008
(Show Context)
Citation Context ...ase with uniformly distributed phases are known. Also, a method for computing the moments of sums and products of Vandermonde matrices, for the non-folded case (i.e., d = 1), has recently appeared in =-=[22]-=-; further insights on the extremal eigenvalues behavior, still for the case of non-folded Vandermonde matrices, can be found in [23]. Moreover, in [9] it has been shown that the LSD of VVH converges t... |

2 | Asymptotic analysis of multidimensional jittered sampling
- Nordio, Chiasserini, et al.
- 2010
(Show Context)
Citation Context ... V to grow to infinity while the ratio of its number of rows to its number of columns tends to a finite limit, β, greater than zero, i.e., we assume lim n,m→∞ βn,m = β Indeed, in our recent works [8]–=-=[10]-=- it was shown that this asymptotic model provides a tight approximation of the MSE of the finite size system, already for small values of n and m. Under these conditions, we therefore define the asymp... |

1 |
Asymptotic behavior of random Vandermonde matrices with entries on the unit circle
- Ryan, Debbah
- 2009
(Show Context)
Citation Context ...es the MSE (i.e., the LMMSE filter) [8]–[10]. The matrix representing the sampling system, in the following denoted by V, results to be a d-fold Vandermonde matrix1. By drawing on the results in [9], =-=[11]-=-, we derive both the moments and an expression of the limiting spectral distribution (LSD) of VVH, as the size of V goes to infinity and its aspect ratio has a finite limit bounded away from zero. The... |

1 |
On energy-aware dynamic clustering for hierarchical sensor networks
- Kim, Lee, et al.
- 2005
(Show Context)
Citation Context ... deployed over a square region. We also identify L areas, Ai i = 1, . . . , L, each corresponding to a different value of the offered traffic load. As often assumed in the literature (see e.g., [26], =-=[27]-=-) and widely applied in the practice, the network is divided into clusters and a hierarchy of clusters is created. More specifically, at the first hierarchical layer, layer 1, the sensors are grouped ... |