What is the effect of the distance between sensors?

In particular, as sensors become more distant from each other, the spatial correlations between their measurements will decay rapidly.

What is the scale–j scaling value of np?

Using its scale–(j + 1) scaling value and those from its neighbors, np computes its scale–j wavelet value asdj,np = sj+1,np − pj,np sj+1,N (np), (6)where sj+1,N (np) is a column vector of scaling coefficients.

What is the scale–j scaling value of the scale–j wavelet?

Using its scale–(j + 1) scaling value and the scale–j wavelet values from its neighbors in N (nu), nu computes its scale-j scaling value assj,nu = sj+1,nu + uj,nudj,N (nu), (7)where dj,N (nu) is a column vector of wavelet coefficients.

What is the way to remove the smallestscale (-area) points at each transform?

Since multiscale analysis provides increasingly broad views of a measurement field at each scale, it follows naturally that the authors should remove the smallestscale (-area) points at each transform level.

What is the scale–j scaling coefficient for a node?

When the measured field is transformed to scale j, each predicted node np merely waits for nodes in N (np) to send their scale–(j + 1) scaling coefficients before computing its scale–j wavelet coefficient.

What is the problem with a two-hop communication path between vertices?

Allowing a two-hop communication path between these vertices does not present a problem in their application; indeed, paths between vertices will generally become multi-hop as the transform scale becomes coarser.

How many edges of the perfect DT have lengths within twice that radius?

the node density and communication radius will both be sufficiently high so that most edges of the perfect DT have lengths within twice that radius.

What is the simplest way to compute the scale–j scaling function for a node?

to compute the integral of the scale–j scaling function for an updated node nu, the authors add the integral of its scale–(j + 1) scaling function to a weighted sum of the scale– (j + 1) scaling function integrals of its predicted neighbors.

How do the authors compute the scaling functions at scale j?

Computing the update coefficients, to follow shortly, requires maintaining integrals of the scaling functions at scale j in terms of integrals of the scaling functions at scale j +

What is the scale–j scaling function integral for a node?

Xnk∈N (nu)p j,nk (nu)Aj+1,nk , (4)where N (nu) describes the neighbors of nu whose wavelet coefficients are predicted at scale j; pj,nk (nu) gives the predict co-efficient node nk applies to the scale–(j + 1) scaling coefficient of node nu.

What is the way to determine the optimal path?

It employs a 1-D wavelet decomposition along a path through the 2-D measurement field; however, no method for determining the optimal path is given.

Open AccessProceedings Article10.1109/SSP.2005.1628777

Distributed wavelet transform for irregular sensor network grids

R. Wagner, +3 more

- 17 Jul 2005

- pp 1196-1201

TL;DR: A new distributed wavelet transform based on lifting that takes into account irregular sampling and provides a piecewise-planar multiresolution representation of the sensed data is developed.

Abstract: Wavelet-based distributed data processing holds much promise for sensor networks; however, irregular sensor node placement precludes the direct application of standard wavelet techniques. In this paper, we develop a new distributed wavelet transform based on lifting that takes into account irregular sampling and provides a piecewise-planar multiresolution representation of the sensed data. We develop the transform theory; outline how to implement it in a multi-hop, wireless sensor network; and illustrate with several simulations. The new transform performs on par with conventional wavelet methods in a head-to-head comparison on a regular grid of sensor nodes

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Most frequently asked questions

1. What have the authors contributed in "Distributed wavelet transform for irregular sensor network grids" ?

In this paper, the authors develop a new distributed wavelet transform based on lifting that takes into account irregular sampling and provides a piecewise-planar multiresolution representation of the sensed data.

2. What are the future works mentioned in the paper "Distributed wavelet transform for irregular sensor network grids" ?

The authors have developed a fully distributed, irregular-grid wavelet transform and protocol for sensor networks that is capable of piecewiseplanar multiscale approximation.

3. What is the performance of the transform coefficients?

The transform coefficients have desirable performance under threshold-based processing such as distributed compression and even perform competitively with centralized, regular-grid wavelettechniques.

4. What is the effect of a distributed triangulation on the mesh?

When the node density and communication radius allow the distributed triangulation to capture all but the longest edges on the boundary of the DT, re-triangulation of the mesh after decimation follows easily using the technique of [15].

Fig. 1. Triangulated mesh of sensor nodes (a) at scalej nd (b) at coarser scalej − 1 (• denotes vertices to be decimated).

Fig. 5. Results of nonlinear approximation experiments. Mean square error (log-scale) is plotted on they-axis with the number of approximation coefficients used in the reconstruction on thex-axis. We note the rapid decay of the approximation error of (a) the noisy, discontinuous quadratic field and (b) the smooth Gaussian bump field. Performance is comparable to more traditional biorthogonal CDF(2,2) wavelets on square-grid sampling for (c) the noisy, discontinuous quadratic and (d) smooth Gaussian bump fields.

Fig. 4. Test data fields: (a) noisy quadratic bump with discontinuity, and (b) Gaussian bumps on a smooth, quadratic field.

Fig. 3. Communication at scalej between predicted (•) and updated (◦) nodes repeated during each wavelet transform. Messages are labelled between a predicted nodenp and an updated neighbor nu. (a)nu sends its scale–(j + 1) scaling coefficientsj+1,nu to each predicted neighbor; (b)np sends its scale-j wavelet coefficientdj,np value to each updated neighbor.

Fig. 2. One-time communication at scalej between predicted (•) and updated (◦) nodes during filter coefficient calculation. Messages are labelled between a predicted nodenp and an updated neighbornu. (a)nu sends its(x, y) coordinates to each node it predicts; (b)np sends its weighted areap

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- 01 Apr 2013

- IEEE Transactions on Signal Processing

TL;DR: This paper extends to signals on graphs DSP and its basic tenets, including filters, convolution, z-transform, impulse response, spectral representation, Fourier transform, frequency response, and illustrates DSP on graphs by classifying blogs, linear predicting and compressing data from irregularly located weather stations, or predicting behavior of customers of a mobile service provider.

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References

•Journal Article•10.1145/844128.844143

Fine-grained network time synchronization using reference broadcasts

Jeremy Elson, +2 more

- 09 Dec 2002

TL;DR: Reference Broadcast Synchronization (RBS) as discussed by the authors is a scheme in which nodes send reference beacons to their neighbors using physical-layer broadcasts, and receivers use their arrival time as a point of reference for comparing their clocks.

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2.6K

Journal Article•10.1137/S0036141095289051

The lifting scheme: a construction of second generation wavelets

Wim Sweldens

- 01 Mar 1998

- Siam Journal on Mathematical Analysis

TL;DR: The lifting wavelet as discussed by the authors is a simple construction of second generation wavelets that can be adapted to intervals, domains, surfaces, weights, and irregular samples, and it leads to a faster, in-place calculation of the wavelet transform.

...read moreread less

2.2K

•Proceedings Article•10.1145/1031495.1031498

A wireless sensor network For structural monitoring

Ning Xu, +6 more

- 03 Nov 2004

TL;DR: Wisden incorporates two novel mechanisms, reliable data transport using a hybrid of end-to-end and hop-by-hop recovery, and low-overhead data time-stamping that does not require global clock synchronization.

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•Journal Article•10.1145/972374.972396

Coping with irregular spatio-temporal sampling in sensor networks

Deepak Ganesan, +3 more

- 01 Jan 2004

TL;DR: In this article, the authors make the case for the existence of such irregular spatio-temporal sampling and show that it impacts many performance issues in sensor networks, such as data aggregation schemes provide inaccurate results, compression efficiency is dramatically reduced, data storage skews storage load among nodes and incurs significantly greater routing overhead.

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147

•Journal Article

Multi-Resolution Storage and Search in Sensor Networks

Deepak Ganesan, +4 more

- 05 May 2007

- Center for Embedded Network Sensing

TL;DR: In this paper, a lossy, gracefully degrading storage model is proposed for in-network storage and distributed search in WSNs, which supports both progressive data collection for interesting events as well as long-term storage for innetwork querying and processing.

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108

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Distributed wavelet transform for irregular sensor network grids

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Most frequently asked questions

1. What have the authors contributed in "Distributed wavelet transform for irregular sensor network grids" ?

2. What are the future works mentioned in the paper "Distributed wavelet transform for irregular sensor network grids" ?

3. What is the performance of the transform coefficients?

4. What is the effect of a distributed triangulation on the mesh?

5. What is the effect of the distance between sensors?

6. What is the scale–j scaling value of np?

7. What is the scale–j scaling value of the scale–j wavelet?

8. What is the way to remove the smallestscale (-area) points at each transform?

9. What is the scale–j scaling coefficient for a node?

10. What is the problem with a two-hop communication path between vertices?

11. How many edges of the perfect DT have lengths within twice that radius?

12. What is the simplest way to compute the scale–j scaling function for a node?

13. How do the authors compute the scaling functions at scale j?

14. What is the scale–j scaling function integral for a node?

15. What is the way to determine the optimal path?

Figures

Citations

Graph Signal Processing: Overview, Challenges, and Applications

Discrete Signal Processing on Graphs

Graph Signal Processing: Overview, Challenges and Applications

Distributed Compressive Sensing

Distributed Compressive Sensing

References

Fine-grained network time synchronization using reference broadcasts

The lifting scheme: a construction of second generation wavelets

A wireless sensor network For structural monitoring

Coping with irregular spatio-temporal sampling in sensor networks

Multi-Resolution Storage and Search in Sensor Networks

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